Grains aren't bad - it's just that some dogs don't do well w/ some grains since dogs are carnivores, so grains aren't a "big" part of a carnivore's diet.
It sounds like she could have some kind of allergy -
which kind at this point is hard to tell (food, seasonal, environmental). I would really try to find out which, bc allergies can have a domino effect...and then more allergies set in.
If you want to try a mid-range protein, grain free diet - one to think about would be Wellness CORE (either regular or Ocean). This is not a true elimination diet at all...but...it may help guide you where to go next in terms of food or whatever. And just fyi, when you make food changes - it can take up to 3mths to truly see results w/ allergens. If you do change the food, I would eliminate those wheat based treats too.
I think most importantly though - has her skin been thoroughly evaluated by the vet? Bc I'd rule out yeast, fungus, and parasites before anything else, to be honest.