If your sick fish is schooling and eating he will probably be okay. I'm not sure what's wrong with him but I'm going to guess it has something to do with him living in poor quality water before you bought him. I read somewhere that swollen gills can be a sign of chemical exposure, which also might explain the fungus like lesions and why your salt dips worked so well to heal them up. I doubt you have enough ammonia in your tank to prolong the gill problem or hurt any of your fish.
I would go ahead and plant now while keeping your fish in the tank. The only stress on your fish would be your hand in the tank, which isn't really any different than siphoning the gravel. If you do have a slight ammonia problem the plants will take care of it as soon as they start getting some new growth. If you are really worried about it you could temporarily add a clump of hornwort and dose the tank with Prime for the first several days to make sure you have ammonium instead of ammonia in your tank while your permanent plants get established.
I would go ahead and plant now while keeping your fish in the tank. The only stress on your fish would be your hand in the tank, which isn't really any different than siphoning the gravel. If you do have a slight ammonia problem the plants will take care of it as soon as they start getting some new growth. If you are really worried about it you could temporarily add a clump of hornwort and dose the tank with Prime for the first several days to make sure you have ammonium instead of ammonia in your tank while your permanent plants get established.