There is a very simple skin test/scraping your vet can do that will confirm or rule out yeast/parasites.
It only takes a minute.
My dog has had the same issues as you described and the test was negative. However she does have environmental allergies and has had positive results by seeing a veterinary dermatologist.
I would consider Purina Pro Plan Focus for sensitive skin and stomach as I have heard good things about it.
I would avoid potatoes of all kinds as that seems to work for one of my dogs. I have heard others say so too.
Good luck.
