I usually don't use chemicals, but melafix might be your best bet to heal the wounds.. I would boost up the temp and add salt before hand to see if that helps. Also, if you're worried about your BB, use a hospital tank.
I use to keep piranhas for awhile and have had alot of nasty fin and body bites, I have have always used melafix and it cures it fast!
Also melafix doesnt harm your bacteria, just make sure to either take out your carbon from your filters before you dose the tank, or like the fella above said, dose up a hospital tank, if you feel more secure doing that instead