I recently got a new betta almost a week ago from PetCo I've done my research on betta and the condition they are in at pet stores. Doing everything to make the acclimation process as painless as possible for him he seemed fine. A few days later I notices a small hole in is dorsal fin and thought that maybe it was already there when I bought him and I just didn't realize it. Anyways as the week progressed I noticed that his tail fins started to look stringy and shredded. It doesn't seem that he has fin not but I'm not sure what is causing it.

A little more about my tank
I do have a small filter
3 Red wag swordtails
1 tetra

--All my other fish I bought the same time as my betta and they all get along fine

Any advise is appreciated greatly.