First, separate your Cory and put in a hospital tank, if you can, so you are just treating him. Mechanical filtration is recommended. Do not use charcoal. A combination of formalin and malachite green can treat a fungus. National Fish Pharmaceuticals has a good one. API has a powder mix of Victoria green and Acriflavine that is also recommended for fungus. Fungus is often a secondary problem so examine him carefully. Fungus is usually not contagious and often grows on an injury when the the protective coating on a fish is compromised. Are you sure it is not columnaris? Does he have tufts on his mouth? Columnaris is a bacterial infection that often looks like a fungus. If it is, the acriflavine may work but the forma green will not. Inverts may sensitive to these meds!
Doing water changes helps keep disease low. You might have to step up water changes in the future. Even in the best kept tank a fish can get sick, especially if the fish has an injury.
Hope he gets well.