This is what I would do, and I have been dealing with allergies in a young dog too, but luckily I have a jump on things.....
I would put her on a homemade elimination diet. It's a little tricky being young and you don't want to mess up the diet, but things are already messed up. I would find a protein, and either over-cooked rice, or steamed green beans. I prefer the green beans and meat as a base diet. Will need to find a multi vitamin and add some calcium and a bit of potassium, but the commercial foods aren't going to cut it.
Have her lay only on things with sheet coverings. I was going to say use cotton sheets, but heck, my last dog was allergic to cotton, but try to make sure that she is not on the new carpet.
Atopica is a scary drug, and it sounds like they are just throwing drugs at her. I would want a couple of things done.
I first want a vet that will work with me. If I ask for a blood panel, even if it's just to make me feel better, I want the vet to honor that request. If the vet doesn't honor that, particularly in a dog that is having problems, that vet needs to be fired.
I would want blood drawn and sent to Dr. Dodds for a full thyroid panel. I would also want a blood allergy test done (some say they are controversial, but they are extremely helpful), and my vet humors me and lets me send the blood off to Spectrum labs. These are things I request of my vet, have them draw the blood, and I ship the blood myself to save money (though the vet has to set up an account with Spectrum, this is not true for Dodds). I also would want a blood test run, since this young dog has been on pred and Atopica.
I would want to see a holistic vet, though I know of none in your area. If I can't see a holistic vet, I am off to a Dermatologist, because if I'm dinking around with these issues, I want to be consulting with someone that specializes in these things.
The quality of food is important here. For example, a deficiency of zinc, caused by high grain diets in certain breeds (nordic backgrounds primarily), will cause a lot of skin issues. But then again, too much zinc is toxic. There are many things to consider here.