I'm not an expert by any means but as long as you are confident you have a pure bred Yorkshire Terrier with papers to support that, if it were my dog and there was an issue with his skin like that, and I felt confident he was causing allergic reactions, I would have him at a good vet like yesterday to find out what's wrong.
I don't think that's normal or common at all and should be treated as a sign of something more serious with his health or something in his environment causing a severe skin problem.
I was really hoping some of the resident experts and breeders would chime in. Hint, hint.