I just saw how long this is... SORRY!
I'll try to answer much of this the best I can (remember -- I've been ER for 3 yrs, not daily skin stuff - but it hasn't changed much in three years!). Skin problems are one of the most frustrating and common problems we vets encounter! It is one of the things I miss least about being a day-practice vet!

Dietary changes take 4-6 weeks to make a difference sometimes -- hang in there.

I do have concerns about "protein free" -- what is the source of protein and be sure it is enough (ie, the side of the bag should have AAFCO regulations posted). otherwise you could end up with worse problems. We typically began a single protein source and did that for 6 weeks before deciding if it was helping or not.

There are some great over-the-counter diets that I've seen make a huge difference in some pets without any previous testings... Wellness WhiteFish and Sweet Potato. The VanDyke limited allergen brands listed by someone else are also pretty good.

Fish Oil supplies large amounts of Omega 3/6 Fatty Acids which are excellent for the skin, as well as many other parts of the body! If there is an allergy to fish, obviously, Flaxseed is a better choice. But the fish is a more balanced 3/6 ratio for them.

Don't forget that you can use anti-histamines for itching when it is bad -- plain diphenhydramine (ie, benadryl) -- without any additives of cold / pain relief -- can be very helpful at 1mg/pound or less. You may give this 1 to 3 x daily to a healthy pet (check with your vet), and when used with the fish oil is an excellent combo.

Blood tests: Skin testing is the gold standard for allergy testing of any kind. Blood tests are not supposed to be quite as good for inhaled allergens, and I've read many times that food allergens are not able to be tested with blood or skin testing. Dietary elimination is the gold standard here. Don't spend your money of blood "food allergy" tests -- it is a waste. However, sometimes these guys also have inhalant or topical allergies, also, and skin testing or blood testing may help you figure this out. I would see a skin specialist for this if you are considering it. It is money well spent.

Prescription diet -- there are several very good diets on the market that are Rx at your vet's office....
IVD makes wonderful hypoallergenic diets: Venison and Potato is excellent
Science Diet makes a z/d that I use in Last Case scenarios: It is chicken but they put it through "hydrolization" which means that it breaks the proteins into tiny pieces, too small for the body's immune system to recognize, and therefore it will not create an immune response. Sounds great, but there are some side effects in several dogs -- you must introduce it very slowly / transition... or diarrhea / gas can be a huge problem.

Bathing can help -- there are prescription shampoos that put EFA's onto the skin and are soap free / hypoallergenic. There is also benadryl shampoo and conditioners that help with itching. Relief spray has colloidal oatmeal and is helpful

Stay away from steroids as much as possible. Way too many side effects! In terribly severe cases they can be useful as short term relief until you can get a handle with other treatments, but do NOT use these regularly. Many dogs end up with diabetes following long term steroid use, and there are many other problems that it can create.

And as someone else mentioned -- always use flea treatment in these guys -- they cannot handle even one b/c they are so sensitive!

Hope this is useful information. Good Luck.
Jes