Jon Snow:
Jon would blush softly and whisper a thank you every few minutes. He would answer all of your questions about how much pain he was in and how he had been injured honestly and reassure you over and over that he was alright. Even apologize for taking up your time although patching him up is "kind of" apart of your job description.
Robb Stark:
Robb would let his "Kingly" guard down and let you see how much pain he was in. He would concentrate on your voice and the feeling of your arm hands on his skin. He would tell you stories about his childhood, his parents, and his siblings. He would have you both laughing and after a while he would forget he had been in pain in the first place.
Joffrey Baratheon:
Taking care of Joffrey would lead to sex...lots and lots of sex. Most of the time you would barely get half of his injury(ies) bandaged before he was instigating something. Afterwards, he would kiss you rough and passionately and thank you for caring for him.
Theon Greyjoy:
Theon would smirk the entire time and suggesting other ways that you could "make him feel better." He would hide how much pain he was truly in even when it was so agonizing behind flirts and abrasive language. But once he was patched up he would blush softly and thank you for helping him, letting down some of his arrogance and showing you the "real" Theon Greyjoy.
Jamie Lannister:
If it was after Jaime lost his hand, he would push you away (not so gently) yelling about how you should just leave him alone. Let him die. He wasn't any use to anyone now without his sword hand. Even after you had wrapped up his stump and made most of the pain go away, he would just glare and mumble under his breath about "stupid wrenches."
Sandor 'The Hound' Clegane:
Sandor would mumble under his breath and roll his eyes, gently pushing you away and snapping about being "fine" and not needing to be babied like a "stupid cunt." But in the end he would bite his tongue and let you patch up whatever injury he has. And once you were finished, he would place a kiss to your head and thank his "little dove" for once again taking care of him.