I agree. A board certified dermatologist is in order. I don't want to worry you unnecessarily, but there is a skin infection in dogs called MRSP, which is related to MERSA in people, though not as bad. But it is often seen on dogs' faces, and does require antibiotics to treat. But it needs to be the RIGHT kind of antibiotics, because, like MERSA in humans, it is Meticillin resistant which also means it is resistant to other, commonly used ABX.
Two separate dogs who train in our area have been DX'd with this in recent months. One was very sick, and required hospitalization before they figured out what it was. The other dog was just chronically sore, scabby, and itch on his face and feet for MONTHS, and treated ineffectively for months before a board certified dermatologist figured it out and got him on the right ABX. He will have to have extended ABX treatment, but he, too, is now on the road to recovery.
I am sure there are other possibilities, and a good dermatologist will help you figure it out. But I thought I'd mention this, because these two dogs suffered for a long time before someone figured it out!