I would definitely quaranteen the one with the skin problem. Just in case it does get infected, you don't want the infection to spread to the other gecko. I would also have them properly sexed, as to find out if they are both males. I would keep them seperated until you find this out. Usually taking them to a herp vet can get all your initial problems taken care of (e.g sexing, fecal exam, etc).
As for the infection on his head, if it looks like a open sore, I would rub some hydrogen peroxide on it with a q-tip very gently. And after that I would give him a warm soak in a bath (with water that goes up to the tops of his legs). And just drizzle some water over his head so that it will fall down his nose and not into his eyes. Then rub some neosporin on the wound after the bath (VERY thin layer).
Males will fight no matter if they are raised together or not. Reptiles for the most part or territorial animals, and loners. They do not NEED companionship, nor do they want it. Although in the past I have housed male geckos together with minimal fighting it was because I had multiple basking spots, and there was never a need for food competition. Even with these amenities there was still minor squabling (usually over which one was eating the most crickets!).
Anyways, I would highly suggest a vet visit for both your little guys. Shouldn't run you more than 50-60$, and an hour of your time for a checkup on both of them.