All this talk of melafix, antibiotics, and rid all is absolute nonsense for a caudial fin injury.
It may assist in healing the fish, but at the expense of destroying your bio filtration and changing your water from pristine to sewer. Don't use these types of medication unless you really have a condition that warrants the use of such medication.
Good water quality is all that is needed to assist the fish in healing. If the injury was so severe and you thought it necessary, you could add a little aquarium salt to assist.