Hi. Did you ever get an answer about what was going on with your cat? My cat has the exact same thing. The vet prescribed an anti-biotic and it didn't work. They took some of his skin and couldn't find an answer. This picture was taken last year. We tried anti-biotic pills, creams, coconut oil. It eventually went away and we thought it was going to be fine. But now the past month its back again and he is scratching them open. He doesn't scratch often but when he does, he scratches hard with his claws. It isn't ringworm as none of our other cats or dogs or us have them and he is the cat that loves and rubs up on EVERYONE in the house. It's only spreads on his nose and ears. No where else on his body.
The picture attached - it was still ok here. Right now it's quite bad. I will try get another photo of him sometime to show how bad it gets. Yesterday he had some blood on his paw and I saw he had scratched one of the sores open on his nose.