Have you tried gluten, dairy and soy free? It could be dairy or soy, or a combination of the three. Some people who were diagnosed officially with celiac disease didn't start getting better until eliminating dairy, and some of them had to cut out soy as well before improving.
I also get the symptoms you mentioned from nightshade foods (potatoes, tomatoes, peppers, eggplant) and from rice and eggs as well.
Your symptoms could also indicate candida.
Don't give up so easily. Something is causing your symptoms, and I doubt that probiotics will fix them (even though they could be helpful - but not on their own.... which is just my opinion, of course).
Have you considered testing with
Enterolab? They will pick up gluten intolerance that is non-celiac, while the tests most doctors do will only identify celiac disease with already advanced villi damage.