Also posted on Tumblr: https://www.tumblr.com/blog/librarychick94
Okay, here are some I found looking through my files. They are in no particular order. I've split them into Gen and McShep, though. Some of the authors listed love to whump Sheppard, so once you try one story, you may find lots more. I also realized I listed some sick Sheppard as well as hurt Sheppard. I did my best on the team part of the request. Please heed all warnings and know that this is just a very few of what is out there. Hopefully more people will respond! Oh yeah, and there is always this: http://sheppard-hc.livejournal.com/
McShep
Fundamentals of Shipwreck Prevention by candle_beck
Summary: John falls head over heels, but literally this time.
http://archiveofourown.org/works/166364
Gravel Road by candle_beck
Summary: Unexpected plot twists, John Sheppard's hair, and other things that annoy Rodney McKay.
http://archiveofourown.org/works/178037
Bare by sheafrotherdon
Summary: John. The name seems solid if not familiar, a passable identity – nothing about it makes him cringe, at least, and he's been called other things (he thinks) these past few days that weren't so benign.
http://archiveofourown.org/works/117987
Breath by sheafrotherdon
Summary: John regains consciousness in a tumble of noise and memory. Vegas tag.
http://archiveofourown.org/works/117957
White by sheafrotherdon
Summary: John half hears them coming, their boot steps quick, furtive; he strains to focus, to bring his thoughts back online, to ready himself to help, but when he shifts there's a burst of pain that ricochets across his temple and he slumps back against the wall, gritting his teeth, letting the manacles bear his weight.
http://archiveofourown.org/works/117960
Suddenly at Last by yin_again
Summary: It took Elizabeth nineteen days to negotiate John's release.
http://www.wraithbait.com/viewstory.php?sid=4703&chapter=1
Tap, Rack, Bang by bomberqueen17
Summary: If you expect it to go bang and it goes click, keep it pointed in a safe direction and call for help.
http://archiveofourown.org/works/988103
Eventual Thaw by zinnith
Summary: The main reason John decides to break up with Rodney is to avoid being dumped first.
http://archiveofourown.org/works/86298
Better with the Lights On by annezo
Summary: John & Rodney wake up in the dark. Scientist-hysteria, epi-pens, and stupidity.
http://archiveofourown.org/works/602661
Accident Prone by ladyra
Summary: Something goes wrong during one of John's missions with his new Stargate team. (Set during The Return)
http://archiveofourown.org/works/927025
Mend by mdime02
Summary: John Sheppard landing in the infirmary was nothing new, but when he finds himself sidelined by mysterious injuries he can’t recall receiving it's a race against time to find the cause...and save his life.
http://sga-santa.livejournal.com/246453.html
Pressure Points by crownglass39
Summary: John never knew a headache could hurt this bad. Episode tag to Common Ground.
http://archiveofourown.org/works/565896
Gen
Once Upon a Time by T’Pring
Summary: Once upon a time, a certain John Sheppard hit his head. Well, a tree hit his head. In a lightning storm a mile from the stargate. At night. Huddled in a cave with a very befuddled John, his team must figure out how to get him home.
https://www.fanfiction.net/s/7255318/1/Once-Upon-A-Time
Burning Man by coolbreeze1
Summary: Sheppard spends a long night incapacitated, with only his team to look out for him. Shep whump, team love.
http://coolbreeze1.livejournal.com/58931.html
or
https://www.fanfiction.net/s/5336769/1/Burning-Man
The Edge of the Bridge by sealie
Summary/note: A fic for Susn, who wanted h/c fic where Carson was competent, Sheppard was the victim, and Rodney to be Rodney. By request this is heavy on the medical details and it’s linear.
http://archiveofourown.org/works/252092
Orpheus Rising by everybetty
Summary: Rodney and the team work to bring John home, then fight to bring him out of the darkness. Set post S5.
https://www.fanfiction.net/s/6766540/1/Orpheus-Rising
The Waiting Game by tridget
Summary: Sheppard and McKay are stuck in a prison with no way out and no rescue in sight.
http://archiveofourown.org/works/413019
Cakewalk by busaikko
Summary: Rodney wanted John's first mission after his return from Earth to go well. It didn't.
http://archiveofourown.org/works/89561
Ars Arboreous by mahoni
Summary: Sheppard is captured off-world by something the Ancients left behind.
http://archiveofourown.org/works/14495
A World Called Catastrophe by perspi
Summary: When the world ends in a flash of orange and yellow, the last thing John feels is the sensation of flying.
http://archiveofourown.org/works/77935
Misdirection by artisticabandon
Summary: Never trust uninhabited planets and natives who have the advantage of home ground. Or, the reason why Rodney never thought John would remember his password. Team fic. Shep whump.
https://www.fanfiction.net/s/8910533/1/Misdirection
Coulda, Would, Shoulda by liketheriver
Caring for your injured CO isn't the easiest job for a Marine. And Sheppard's isn't the only team on Atlantis.
http://sga-flashfic.livejournal.com/824414.html
Revised Diagnosis by alipeeps
Summary: tag to Search & Rescue
https://www.fanfiction.net/s/4353771/1/Revised-Diagnosis
Okay, here are some I found looking through my files. They are in no particular order. I've split them into Gen and McShep, though. Some of the authors listed love to whump Sheppard, so once you try one story, you may find lots more. I also realized I listed some sick Sheppard as well as hurt Sheppard. I did my best on the team part of the request. Please heed all warnings and know that this is just a very few of what is out there. Hopefully more people will respond! Oh yeah, and there is always this: http://sheppard-hc.livejournal.com/
McShep
Fundamentals of Shipwreck Prevention by candle_beck
Summary: John falls head over heels, but literally this time.
http://archiveofourown.org/works/166364
Gravel Road by candle_beck
Summary: Unexpected plot twists, John Sheppard's hair, and other things that annoy Rodney McKay.
http://archiveofourown.org/works/178037
Bare by sheafrotherdon
Summary: John. The name seems solid if not familiar, a passable identity – nothing about it makes him cringe, at least, and he's been called other things (he thinks) these past few days that weren't so benign.
http://archiveofourown.org/works/117987
Breath by sheafrotherdon
Summary: John regains consciousness in a tumble of noise and memory. Vegas tag.
http://archiveofourown.org/works/117957
White by sheafrotherdon
Summary: John half hears them coming, their boot steps quick, furtive; he strains to focus, to bring his thoughts back online, to ready himself to help, but when he shifts there's a burst of pain that ricochets across his temple and he slumps back against the wall, gritting his teeth, letting the manacles bear his weight.
http://archiveofourown.org/works/117960
Suddenly at Last by yin_again
Summary: It took Elizabeth nineteen days to negotiate John's release.
http://www.wraithbait.com/viewstory.php?sid=4703&chapter=1
Tap, Rack, Bang by bomberqueen17
Summary: If you expect it to go bang and it goes click, keep it pointed in a safe direction and call for help.
http://archiveofourown.org/works/988103
Eventual Thaw by zinnith
Summary: The main reason John decides to break up with Rodney is to avoid being dumped first.
http://archiveofourown.org/works/86298
Better with the Lights On by annezo
Summary: John & Rodney wake up in the dark. Scientist-hysteria, epi-pens, and stupidity.
http://archiveofourown.org/works/602661
Accident Prone by ladyra
Summary: Something goes wrong during one of John's missions with his new Stargate team. (Set during The Return)
http://archiveofourown.org/works/927025
Mend by mdime02
Summary: John Sheppard landing in the infirmary was nothing new, but when he finds himself sidelined by mysterious injuries he can’t recall receiving it's a race against time to find the cause...and save his life.
http://sga-santa.livejournal.com/246453.html
Pressure Points by crownglass39
Summary: John never knew a headache could hurt this bad. Episode tag to Common Ground.
http://archiveofourown.org/works/565896
Gen
Once Upon a Time by T’Pring
Summary: Once upon a time, a certain John Sheppard hit his head. Well, a tree hit his head. In a lightning storm a mile from the stargate. At night. Huddled in a cave with a very befuddled John, his team must figure out how to get him home.
https://www.fanfiction.net/s/7255318/1/Once-Upon-A-Time
Burning Man by coolbreeze1
Summary: Sheppard spends a long night incapacitated, with only his team to look out for him. Shep whump, team love.
http://coolbreeze1.livejournal.com/58931.html
or
https://www.fanfiction.net/s/5336769/1/Burning-Man
The Edge of the Bridge by sealie
Summary/note: A fic for Susn, who wanted h/c fic where Carson was competent, Sheppard was the victim, and Rodney to be Rodney. By request this is heavy on the medical details and it’s linear.
http://archiveofourown.org/works/252092
Orpheus Rising by everybetty
Summary: Rodney and the team work to bring John home, then fight to bring him out of the darkness. Set post S5.
https://www.fanfiction.net/s/6766540/1/Orpheus-Rising
The Waiting Game by tridget
Summary: Sheppard and McKay are stuck in a prison with no way out and no rescue in sight.
http://archiveofourown.org/works/413019
Cakewalk by busaikko
Summary: Rodney wanted John's first mission after his return from Earth to go well. It didn't.
http://archiveofourown.org/works/89561
Ars Arboreous by mahoni
Summary: Sheppard is captured off-world by something the Ancients left behind.
http://archiveofourown.org/works/14495
A World Called Catastrophe by perspi
Summary: When the world ends in a flash of orange and yellow, the last thing John feels is the sensation of flying.
http://archiveofourown.org/works/77935
Misdirection by artisticabandon
Summary: Never trust uninhabited planets and natives who have the advantage of home ground. Or, the reason why Rodney never thought John would remember his password. Team fic. Shep whump.
https://www.fanfiction.net/s/8910533/1/Misdirection
Coulda, Would, Shoulda by liketheriver
Caring for your injured CO isn't the easiest job for a Marine. And Sheppard's isn't the only team on Atlantis.
http://sga-flashfic.livejournal.com/824414.html
Revised Diagnosis by alipeeps
Summary: tag to Search & Rescue
https://www.fanfiction.net/s/4353771/1/Revised-Diagnosis