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Probably not it, but this sounds reminiscent of Jeremy Thatcher, Dragon Hatcher by Bruce Coville (of My Teacher Is an Alien fame). I say probably not because (if I remember right) the kid who has a pet dragon isn't handicapped and doesn't wet his pants. He is bullied though, and is really short and socially awkward.
I'm blanking on the name of it, but this is vaguely reminding me of a book I read somewhere in the 1990s. The kid had something like cerebral palsy or muscular dystrophy which involved a loss of fine motor control. I remember a scene where a girl he thought was cute was climbing up a ladder to get a book and he realized that he could see up her skirt. That and a section involving a bunch of delinquents who had a clubhouse in the woods. I want to say that they abducted the girl at one point, requiring him to come to their aid. *wry grin* Hopefully the additional details will be of some help to you in tracking it down.
Found it thanks to Fuzzy Boots! Googled "cerebral palsy AND dragon AND book"/ It's Eddie's Blue Winged Dragon. http://www.amazon.com/Eddies-Blue-Winged-Dragon-C-Adler/dp/0595329470

This would have been a Young Adult book from around 1993 or so. It involved a boy who was socially akward or handicapped or something like that. (Maybe he had crutches or leg braces.) There was a magical dragon that only he could see. I think it was from a stuffed dragon, but maybe that's just Homestuck wrecking my memory. The kid was bullied a lot and it was kind of tough to read because he had such a crappy life. I seem to remember him being bullied in the bathroom and peeing his pants.
Not much to go on, but I know you guys work some powerful magic with the interwebs.