Welcome to the forum!
You are right, you should keep eating gluten until the tests are all done. The skin problems you describe ma be a condition only celiacs get. The condition is called dermatitis herpetiformis (DH for short), DH causes an itchy rash that is usually symetrical on the body. You get the rash on both arms or legs etc. It makes little blisters on the skin. They are caused by IgA antibodies in the skin. There i a test for DH where they take a small skin sample (biopsy) from the skin next to a blister and check it for IgA antibodies. If they find DH, then you have celiac disease. The 2 conditions are never separate. there is a section of this forum dedicated to dermatitis herpetiformis with lots more information.
The usual diagnostic process is to do a celiac antibodies blood test first, and then an endoscopy to test for damage to the gut lining. But with DH, it is better to get the skin biopsy done instead of the endoscopy.
Celiac disease is passed on in genes, so your children should be tested also if you are diagnosed.
Research Celiac Ataxia for potential diagnosis.
Look at Milk and dairy for potential head and sinus related issues. I stopped dairy and I can breathe now!
Saturated fat may also be a problem, but it's mostly dairy!
It is best not to try and do this on your own. Talk to your allergist. Not all will deal with food intolerances but if yours doesn't find one who will. Mine had me fill out a very detailed diet questionaire and tested for true allergies before he gave me my starting point. I will admit I wasn't real happy with my starting point since none of my usual foods were on it. He said that I was most likely to react to foods I ate the most so most of the 5 I either rarely ate or didn't really like. The prescribed starting point he formulated was designed to make sure I had adaquate nutrition and enough calories. It took about 2 weeks before a lot of my tummy issues resolved and I was then able to start adding foods in one at a time for a week before moving on to the next. He said food intolerance reactions can take up to a week to show up so I had to be sure it was a full week between food additions.
I did have to call three offices before I found a doctor who could do the formulation of the diet but this guy truely saved my life. Out of all the doctors I had seen, including specialists in big hospitals, he was the one responsible for finally realizing I was celiac. He of course referred me back to my clueless GI doctor who confirmed the diagnosis by almost killing me with a gluten challenge.
I should note that some of my intolerance (not gluten of course) did resolve after I had healed. Even dairy which I hadn't been able to have for years! I hope you can get some answers and are able to heal soon.