I've never personally dealt with fin rot but the conservative treatment is Aquarium salt. Don't use it for longer than ten days, though... Many medications are pretty harsh on them so I prefer to try salt before anything else.
I believe with fin rot you are looking for fin regrowth and the black edges to disappear... I think they turn white at the edges when they are healing? When the fin rot signs go away, then just warm, clean water and possibly stress coat will help with the healing process.