He may be nipping at his fin b/c he's stressed, or hungry etc~ or.... maybe 'just because'! I had a betta who would nip at his tail as much as he could, even though he was living in a comfy home! (or, at least I felt it was.. lol)
I am still somewhat of a n00b on bettafish keeping, but, I believe first step is to treat him with aquarium salt (1/2 tsp/gallon). It can help it heal. You can also try adding Indian Almond Leaves. I have read online that it has 'magical' capabilities in helping bettas heal/keep healthy! If you can't get your hands on some, you can probably find an 'Attison's betta spa kit' at your local fishie store! That stuff contains IAL extract.
I have no idea how to tell when the finrot's gone..... @_@ I mean, finrot is characterized by blackened jagged tips to the fins, so...... if it's 'gone', does it mean these blackened tips magically disappear, and it seems that the fins are growing back? XD I really dont know...