Do not use Melafix or the similar Primafix with fish like cories, characins, and frankly most other soft water species. These products rarely do anything, except by luck, and all medications do negatively impact these fish so the fewer the better.
Do a major water change--provided parameters which are GH, pH and temperature are relative the same between tap water and tank water, a change of 70-75% at one go is way more effective. And may be all that is needed.
As to the fin, see if you can see what may have caused it...another fish nipping? Sitting motionless in front of the aquarium for an extended period (the fish forget you are there if you make no movement at all) can sometimes revel things we don't expect in behaviour. I would watch for fungus, which sometimes appears on injured cory fins, and there is one effective and safe way to deal with that if it occurs, which I will explain if needed.
