Black skirts should be in a school of 6 minimum for good behavior. Yes, they are usually the fin nippers.
Try to get an API Freshwater Master test kit (liquid test kit) and test the water. Most cases of fin rot are from water quality issues.
20% water changes is a pretty small amount especially weekly. For example, Say you had 1 ppm
ammonia and you changed 20% of the water......you'd then have .80 ppm
ammonia. Both would still be bad.
If you could post a picture so we could see how bad it is that would help on treatment. And I do believe you should probably quarantine at this point. It saves you money on meds because of the smaller water volume, it doesn't expose your main tank to potential BB killing meds and takes out your cycle, and if it is from fish nipping you want him away from the culprit so he can heal.