Aww, sorry to hear Dixie is having skin problems, it's so common
Do you have any idea of what causes it? Is it seasonal? I would probably use something else to shampoo her with... something that's suitable for her situation and that's made for dogs. I'm in South Africa so I don't know what brands you guys have over there but I've heard of a special oatmeal shampoo that's supposed to be great. And a last rinse with water containing some Apple Cider Vinegar is great for the skin too.
Do you have a picture?
@2BullyMama (my go to, skin issue guru)