I hope you didn't start it. I think fighting should be done in the ring. If someone does something bad enough to make you want to hurt them severely (like hurt your family or close friends) so be it, if they don't go that far (eg are just a dick or whatever) let it pass.
Yep, you will hurt your hands if you go that path and do damage. Can take a while for the knuckles etc to fix emselves, or if you pressure fracture one of those little bones in your hand.
Hope your recovery goes well (ice, every hour for 15-20 mins I think is the advice) but try not to fight any more, walk away, most people aint worth it. IronMike