Hey Paisleybunny, I had the same issue with my bun couple of days ago. Did the part of the nail that was broken fall down or is still hanging? Mine had it hanging so the vet removed it. I would also advise going to the vet at least for a check up , and then if you are able to handle and medicate him at home probably you could do it – I am not very able to handle him so I prefer vet. Regarding the licking , from what i know is bad. If the bun licks it, it will take longer to heal and might also get infected from bacteria thats in the saliva. Also if he doesn’t let you touch his paw means the bun is in pain so you should as Muchelle said, give him something for the pain.
You can take a look at what the good people of this forum suggested to me on the thread ‘Broken nail and aftermath’ if you want.
But, once again, as Muchelle suggested , maybe you should do a trip to the vet…better safe than sorry.
Basically if all goes well in 1 week tops he should be all good.