The Buteyko breathing method I find helps with both the air hunger/SOB symptoms as well as an ancillary benefit of reducing anxiety. I used to get a lot of anxiety and near panic when air hunger was at its worst. The breathing techniques helped to calm the mind and the breathing.

I would suggest looking into the Buteyko method, or really any other breathing method that focuses on calm, relaxed breathing. Meditation also helps- I think you might benefit from a routine of dedicated, relaxed breathing to see if your symptoms will go aways.

For me, I also would have periods of time early on when the feeling went away completely only for it to return if I was neglecting doing breathing exercises and each time symptoms returned, it would get more difficult for them to go away. Until I realized that I have to manage the condition on a regular basis, which is where I am now.

Let me know how your asthma test goes. I'd be curious to see if there's anything there that could correlate to your symptoms.