Do a very big water change and dechlor with normal dosing.
Then do a round of treatment with a broad spectrum anti-biotic. This may damage the bacteria in the filter. Mardel Maracyn 2 would be an example. You dose it for 5 days. It can be repeated for another 5 if needed.
-You need oxygen in the water, so air power and/or surface agitation is needed.
-Leave your filtration in place. If the problem is bacterial, then it will be in the filter as well as the tank. You should monitor the tank for ammonia if possible. Water changes should protect against it. Bbut, if the filter is being harmed by the treatment, you need to know.
-Lower the temp. close to the bottom of the normal range for this fish. Bad bacteria tend not to like cooler temps.
-After day one, change 50% of the water every day. Vac, up the bottom of the tank at this same time.
-Add each day's medication after the above water change.
Get some fake plants, ceramic or rock decor in the tank so the fish can hide and feel safer. Stress weakens the ability of a fish to fight od disease and parasites etc. You can bleach dip the decor afterwards and use it again if the fish dies. Do not use wood.
If I am correct and the fin rot is bacterial, you should see some improvement in a few days. If this is partial, then do a second round of treatment. Improvement means first stopping further fin erosion and, second, seeing some sign of regrowth.