I would actually switch to the medicine. Meds now a day's are easier on fish than Aquarium salt is and actually AQ doesn't actually cure fin rot. All AQ salt does is stimulate and iritate the slime coat which produces more slime, which means that it's good for keeping parasites off your fish, but doesn't do much for fin rot.
So daily water changes is going to be your fishes best friend for a while until it clears up but you can definitely start the medicine just fine after you take out all the salt. Salt is just too harsh on the system and there are better and easier ways to treat diseases and illnesses now. Salt can also lead to Dropsy because it can cause liver/kidney failure if the fish is not up to par in health and even then sometimes it can hurt. That's more for higher dosages of salt like 3 tsp/gal instead of just 1, but there's still a chance especially if the fish is already been compromised by something else.
So what I'd do is just do a series of water changes over the day to take out all the salt, just small ones like 25% or 50% depending on the size of the tank and then tomorrow you can start the medicine for him