First I'd find out exactly what the boyfriend used on the kitten since he shouldn't have needed to do anything if the litter box was clean. Then you should have the kitten checked out by a vet. The raw areas may have already been there before the kitten fell into the litter but, either way, you need to find out if your dealing with something that is infectious to mom and the other kittens.
When you return from the vet, be sure to take some clothing the mom cat is lying on and gently rub it on the kitten to help her recognize this kitten is hers.

My worry is that the kitten may become so sick it stops nursing, or the mom may reject it altogether.

Let us know what the vet says. Others may have suggestions but I'm curious as to how the vet will treat the kitten so that the mother doesn't lick off any medication or continue to irritate the area. You may end up having to do some supplemental feeding.