Andrea is right, it could be good to have a look at some medication specifically for bettas
But some tend to have their fins nipped in the pet shops by the other fish (unless this one was kept alone) so it may be just physical harm, where you won't have to use any stronger meds than melafix/salt
Some bettas also have a kind of "torn" look on their fins, as they have been bred just for that particular trait. However, it's not very hard to notice whether the fins are healthy or not.
I'd really like to see a photo as well!