Welcome to Yorkie Talk and thank you for rescuing.
Is he on a flea and tick protection, have you checked him for fleas and ticks. If he is on the above he could have dry skin, when you give him a bath, do you use a condition? using a conditioner is not only for their hair, it's for their skin also.
If your answer to the above is yes I also suggest a vet visit. If he's rubbing as much as you say he will start losing hair from all the back rubbing.
It could also be allergies.
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