most require two hands, but some might be easy or slow-paced enough to be playable with one hand. Try turn-based rpgs (Ni no Kuni, but you have to move around in fights) and adventure games (Walking Dead, Back to the Future), Echochrome, Machinarium, Unfinished Swan, Eufloria, Sound Shapes, Papo & Yo, Space Ace... these might be simple enough that you can play them with one hand.
Do you have a DS or 3DS? That'd be your best bet because many games are designed to be playable with just the touch-screen, so you would only need to use your right hand and can just lay the system on the table.
Try one of the turn-based RPGs or SRPGs so you can play at your own pace.
Too bad there aren't things like movies, or books, or taking walks. You know, those things that would help alleviate the boredom of waiting for your hand to heal.
I'll bet you're a joy at the Children's Hospital - "Look Timmy, I know everyone is saying that even though you're handicapped you can still do anything anyone else can do but I'm here to tell you that you can't. Suck on that."