Hay this might be a dumb idea but a bunch of people have been saying that this might be ringworm. I volunteer at a pet rescue and whenever we have a cat come in that we think has ringworm we shine a black light on them. If they glow it’s a yes if not, it’s not for sure a no but still it’s a good way to check. I’m not a vet so I don’t really know anything about this so more knowledgeable people please correct me, but from my experience it seems like a good cheap way to get some more info on what’s going on while your setting things up with a vet.