To a different degree, your experience is similar to mine. I went to the GI doc because my lungs were in horrible shape and my docs were certain it was reflux related. My PH monitor showed very little reflux, and I was told that "my reflux was not causing my asthma".
Fast forward, after years of continued struggle with my lungs, I had another PH monitor, and the reflux amount was a bit higher. Finally, with the continued pressure of my asthma and PCP, the GI doc sent me to a surgeon to discuss the possibility--being sure to tell me that I could continue with meds if I like. That hadn't worked for years, and I knew that surgery was the only answer.
Even the surgeon was concerned about
the fact that my reflux level was very low for surgery.
He said that "if the asthma is caused by reflux, the surgery will help." Low and behold, my lungs did improve, and indeed, the surgery was the answer.
I've had a few bumps in the road because of my severe GERD caused asthma and coughing during recovery, but there is no doubt that I needed the surgery.
Persevere. If you are having problems, don't stop looking for answers.
Good luck, Liz!