Actually, if you have her in warm clean water, she should heal all by herself :) why dose something that is minor? ;) Looks like she has regrowth on her caudal already anyways. She is actually veiltail. See how the anal fin swoops underneath the caudal. That is a trait of a veiltail. The picture attached is my 3 month old baby betta, from a doubletail geno X halfmoon spawn. Note how the anal fin is more streamlined.
Your girl is purty though :3 Name her to match her circumstance, or behavior.
If the clean water way is not working too well, I would use 1-3 teaspoons of aquarium salt PRE DISSOLVED, gradually adding over time so not to shock her. Daily water change and re-adding the salt you take out, in a week she would be looking really great. It also acts as an immune system booster.