USUALLY, yes they do... but remember it will be growing back in from the top of the nail (the cuticle area), and they grow very slowly. some of the old nail may also stay attached to the live nail bed as this is all going on too. If you've damaged that area in particular where the nail BEGINS to grow, it is POSSIBLE that you may never have a nail again - but it's not that likely. If it's still hurting pretty bad, you may want to go to the doctor sooner rather than later. They can put a hole in the nail to release some of the blood underneith the nail - which is likely causing a LOT of pressure/pain. Good luck.
FYI... Katie dropped a can of whipped cream on her big toe on Christmas. It is STILL black under that nail at the cuticle area. It hasn't fallen off, but it's still working it's way on growing out. So, when I say it takes a long time.... it takes a LONG TIME!
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