Absolutely NOT, femmeartist51. I sick fish must have a stable, safe environment in a hospital setting, not a makeshift bucket with salt water. If the fish does not recover on his own, then let him go in peace. Airstones are inappropriate for water circulation and needed oxygenation for salt water aquaria.
You could try and set up a quarantine with pumps, heating, hiding spots and be willing to watch and deal with cycle problems on a daily basis. If you are prepared for that, then we can suggest how to proceed. But you will have to be on top of the situation for the next several weeks every day to do water changes daily. Even with that, you don't have viable water since your display tank has ammonia and you haven't been successful in getting that under control.