Skin issues are an enormous problem with pets today and it can be due to allergies (food, environmental, contact) or may be due to systemic yeast overgrowth. In order to determine which it might be, let's first look at the issue of Contact Allergies.
There are contact allergies you need to consider before you go to all this expense of allergy testing, provided you go that route. Take a careful assessment of any changes in cleaning supplies, detergents, aerosol sprays and carpet sprinkle products. You may just have a"Taa-Da" moment and save youself some major $$ in testing.
I know of a breeder who spent thousands of dollars trying to figure out what was wrong with their show dog. They had this dog back and forth to Purdue with no results. Then one day the owner called and said how his show career was over because of his skin problem and he was the #3 dog in his breed. I knew he was on a very good diet- something else was going on so I flipped through my mental rolodex..... I asked the owner "by the way, do you use Carpet Fresh?" He responded, "Oh yes, 2 -3 times a week, we have two males in the house, you know, I have to!". I said, "Well, more than likely that is your problem, you will need to have your carpets professionally cleaned to have the stuff removed, and bathe the dog with a shampoo from the vet. Rinse in a baking soda rinse and I just bet the dog will be fine. I ran into the owner 6 weeks later at a dog show, with his dog. He was glad to report once they cleaned the carpets and bathed the dog, the skin the problem went away.
Another breeder had changed diets 4 times and after talking it through we figured out the leather cleaner they used on the couch was problematic for their Dobe. If you think you have to use something on your carpet just use baking soda. Tide detergent, as well as other detergents can be a very problematic if used on dog bedding. Just wash bedding in bleach, no soap and NO softeners, which can trigger respiratory reactions in young animals and children. Particularity any aerosol sprays, like air freshener and especially Lysol and other kinds of disinfectants. Do not use them. Yard, flower, bug sprays and sprayed fields in agricultural areas…all of these things can cause serious contact allergy reactions. And lastly, swimming pools with chemicals/chlorine can also be a serious problem for skin and coats. Shaklee has a great line of Green Products for cleaning and they are safe for kids and pets.