I would also recommend seeing a vet. Better to be safe than sorry!
What you're describing does sound similar to my dog's allergy symptoms. (She has a lot of dry skin/dandruff problems, and often gets a rash and loses hair.) Some of my girl's allergies are environmentally based, but most are food-related.
You said you have tried medicated baths to help with the skin issues; have you tried tea tree oil shampoo? That is the only thing I have found so far that helps for more than a day with Lena.
“Once you have had a wonderful dog, a life without one, is a life diminished.”
― Dean Koontz
Lena - Keeshond