Hi QT
It could also me the milk as cows milk is very different from dogs milk and she might be reacting to that
Has she always been itchy or has it started since you had her? What was her breeder feeding her on?
Sorry I know that is more questions but that might help provide the answer. If she hasn't changed food from what her breeder was giving her I would probably try leaving the milk out first before swapping foods.

HTH
Tracy