Hi There,

This sounds more like your cat has experienced some kind of trauma than anything else. A cat would not actually pull out it's own claws, although if claws become stuck in something, like a screen, part of a claw can break off. Sometimes cats that get hit by cars have severely frayed nails because they tend to stretch out their claws on impact.
I think your injured cat is blaming the other cat for the injury, which may or may not be true. Perhaps the cats were near each other when the injury occured.
I know you are keeping a close eye on your injured baby, so infection is unlikely, although if there is a lot of pain involved a trip to the vet may be in order.
I am hoping that there has been some improvement in behavior since you posted.

Take Care,
PHKitkat