Thyroid test came back normal.
She is grouchy and her hair is thin.
Okay who did the thyroid? If in house, have them redone and sent to a legit lab! Because honest, what you describe sounds more thyroid than allergy. I always tell people not to waste money on in house as no matter what, you STILL need the full panel run by a legit lab… if its positive you need full lab to evaluate why and if it's negative they often are falsely so still need to run full.
Approved thyoid labs:
Also, if allergies, often licking is sign of food allergies, especially if benedryl isn't helping. I would look into a limited items food like wellness fish and potato or pinnacle fish and potato. Give them a try.
I don't know much about the allergies but with Zahra's mite skin problem, I switched her food to Eagle Pack Holistic Chicken after talking it over with a trainer. Her coat is now beautiful and the hair is growing back from where she was infected and I have gotten to be rather picky about what the dogs get to eat, if it is does not have good ingredients they are not getting it.
I just wanted to suggest the Eagle Pack Holistic for a good food.