I'd bet $100 it's a fungal infection like ringworm. My pup had it and it started just like you are describing. I've seen many other threads with the same symptoms.
I'd try an over the counter anti-fungal product like lotrimin for about a week. If you don't see improvment get a scraping at the vet. They can give you a prescription that is stronger.
Either way, check your pup's nose and ears for hair loss as this is fungal too.
It seems that yorkies are prone to yeast (fungal) infections - especially when they are young.
Let me know if it helps!
