Yes, if you want to know if you are gluten sensitive then do the stool test through enterolab.com You don't need a doctors order to do it. Many people who test negative for Celiac disease will test positive for the antigliadin antibody via stool. But the proof is in the gluten-free diet. If you improve with the diet than you have your proof.
So glad you're improving but if you want to know if you react to gluten than test. There are also other serum blood tests for IgG antibodies, again they're an out-of-pocket expense. You might look into ALCAT.com, they offer tests for over 300 foods but you need to find someone in your area that will do the blood draw. Not all doctors believe in these kinds of tests because they're variable, meaning one day you might be sensitive to a food and the next week you aren't.
I've have a lot of confidence in enterolab.com, the gastroenterologist who invented the stool test I believe is ahead of the curve in finding gluten sensitivity in those who aren't Celiac but react to gluten.
Congratulations on seeing some relief, keep with it.