Ok; a possible cause of these symptoms in people (which can often translate to the same disorder in dogs)
could be
celiac disease-intolerance of glutens
-try a gluten free diet?
Test: IgA (for autoimmune disorder)
And do a skin biopsy of the rash to check for this:
Dermatitis herpetiformis, a skin rash caused by gluten consumption, is usually (but not always) one of the itchiest rashes you'll ever experience, and lesions can sting and burn as well as itch.
Please let us know what you find out!