Almost definently not Ringworm. Looks nothing like that.
I'd wager a guess that it's Poison Ivy or a more severe than usual reaction to some sort of nettle weed like a Bull Nettle.
It could even be an usual case of an athelete's foot like infection.
Personally, I'd paste that baby up with some calamine and wait a day or two before going to the doctor; especially since you don't seem so keen on doing that anyways, or you wouldn't be asking us.
Some sort of anti-itch cream wouldn't hurt either. Calamine will help that a little. If it's an infection rather than a reaction to a plant, scratching will cause it to spread, even get on your fingers and then spread to other parts of your body or other people.
