That is NOT ringworm. The scab falling off by itself should be enough of a differential diagnosis to tell any medical professional THAT. And I would follow the advice of other posters to NOT take antibiotics until it is tested to see if it a) is bacterial and b) what the proper antibiotic is. Because if it's fungal or a bacterial strain that's resistant to what you're using, you'll just make it worse.

And that does NOT look like something you want to get worse!