His finrot will actually get much better with frequent changes of his tank with fresh, conditioned water. If your tank is only 1 gallon, changing his water every day for a week would not be too often. Spoil him with fresh, conditioned water. :)
Too much salt or using salt too long can damage a betta's liver and cause other difficult issues. Salt is best used as an occasional treatment for specific conditions. In most cases, it is epsom salt, not aquarium salt, that is called for.
You dont always use salt, only if your fish is sick, because they build up a tolerance for it, and when you need it, it wont do a thing for your betta. Salt obviously isnt helping the finrot, so the only thing to do if do 100% water changes every day for awhile (salt-free) to clear things up.