Lots of mums have these sorts of problems and still continue to breastfeed. It's doable It does bloody hurt, though!
If it's happening when you offer, then maybe try waiting till they ask. If it's happening after they've fed for a while, then maybe consider the feed over.
They are clever right from birth and know how to get fed, so it's generally safe to just not allow the feeds if it involves them biting you, if you see what I mean.
Good luck