For the shredded fins add some aquarium salt it will keep infection from getting to them. They will grow back.

It would seem that she has sustained an injury hurting her swim bladder. Their swim bladder keeps them balanced in water. But she might just be constipated. Is she pooing normally? If not starve her for a day and then the next day give her a little bit fo the inside of a pea. This is what usually causes swim bladder disorder(SBD). But like I said earlier it may be an injury from jumping or from being with the other betta. If this is the case then there is no way to really fix it. It is painful just annoying for them. BUT you can make it easier for her. Look here: http://www.petfish.net/kb/entry/155/ C= I am sure she will be okay. *goodvibes*