I wouldn't go for an antibiotic for just a bit of fin rot, if that's even what it is. Like OFL said, some discoloration can be a sign of regrowth, particularly whitish and clear areas. However, if the fin has a black, crusty outline, it is likely infected.
Usually the infection will go away with clean water and warm, stable temperatures. You could use the salt treatment for a few days, but once I see regrowth on the fin, I stop using the salt since long term use of salt puts unnecessary strain on the fish's internal organs.
I would only use antibiotics if the infection was severe and spreading quickly, and the fish was acting lethargic and ill. Using antibiotics comes with consequences--here is a good article that you should really read before you ever use antibiotics to treat your fish: http://edis.ifas.ufl.edu/fa084
it goes over the risks and proper use of antibiotics very thoroughly.