Ringworm is NOT a big deal...
My own daughter who is now 7, had Ringworm from the time she 2, to the time she was 5. Gross huh?
We just COULDN'T get rid of it. We took her to the Dr.s so many times, SO many different prescriptions, nothing worked.
Finally in desperation, I went to a homeopathic Dr. who suggested we use Collodial Silver on it. CS beads up and rolls off of skin instead of absorbing right into it, so on my daughter who only had 2-4 spots at a time, we just put the drops of CS onto a band-aid and then onto the Ringworm spots.
I'm not sure how you would use it on a Dogs stomach, but maybe orally would work, many people take CS orally and we've used it in animals in the rescue orally as a natural antibiotic.
Just don't overdo it, it can make your/his skin turn grey.
Also on Tea Tree Oil, it is harsh on the liver when used straight and for this reason I wouldn't use it straight on skin at all.