I have a cousin who is allergic to gluten but does not have celiac disease, so yes, it's certainly possible you've got an allergy going on.
What kind of doc did your tests? If it was a GI doc looking at your bowel issues, you probably need to go see an allergist/immunologist.
Of course, the cheapest thing (if not hte easiest) to do is just to try an exclusion diet. If you feel better going gluten free, then that's all that really matters in some ways.
I had same situation and separately I was tested for food allergies using IGG and wheat again showed up at a very high sensitivity number. My gliadin was off the chart strong positive; something like 3x or more the higher end number.
Like you, I was told I did not meet celiac based on other testing. on my own, I became 100% gluten free and within a week or two noticed that my symptoms were lessening more and more and more now 6 years later I am still gluten free and my bowel problems are much lessened than ever.