To expand on my opinion of leaving it alone, I do this because when fish get a disease or fungus it is because they are stressed and/or in less than optimal health. If your fish is in good health he won't get a disease or fungus as a result of his injury unless he is really stressed by it. Catching a fish stresses them a lot, and 9 times out of 10 you will make the situation worse no matter your intentions. Many medications also permanently damage the fish's immune system and/or kidneys/liver. Only on rare occasions will I treat a fish for a disease once the fish has been introduced into my tank. I do bath all incoming fish during their drip acclimation with a parasite treatment mostly intended for internal parasites. Once they are in my tank they have to fend for themselves. I will provide them a stress-free environment by choosing appropriate tankmates, a vitamin and garlic enriched diet, and they provide me with many years of healthy existence.
I have treated many a fish for disease, fungus, and parasites in retail stores (as "protocol"), and usually the fish die. This is in part just because of the stress of shipping, and the further stress of being in a retail space, as well as the toxins of the treatment, but also just because if a fish is in poor enough condition to get a disease he is likely on his way out anyway. Only on one occasion have I treated my own fish. That fish was a 6" Piranha with dropsy. Dropsy is usually fatal, but I chose to try to treat him because Piranha are resilient, and I was interested to see if I could cure one of the diseases that is generally considered fatal and "incurable". Halfway through the dropsy treatment the fish actually picked up a nasty case of ich as well, but after three weeks of diligent careful treatment the fish actually survived, and is still alive today about 6 years later.
I don't think your frog fish's condition is very bad at all. With some good food, vitamins/amino acids, and garlic I do think he should snap right back provided he was in good health before the incident.