I, too, suffer from unexplained (at least so far) of shortness of breath. It usually occurs when I bend over, like to tie my shoes, or clean the bathtub, etc. I occasionally have it upon slow exertion, like climbing a hill at a walk. I o do have larger than normal lungs (so called hyperinflated) and a barrel chest. Been that way since I was a teen. My father passed from COPD and was a smoker. We lived in a home heated by a wood-burning fireplace. In retrospect, it shouldn't be surprising that at 65 I am having issues.
I have recently discovered different breathing programs that have really made a difference for me. A long breath in (10 beats or more) through the nose, then a long breath out through the mouth of the same duration. The controlled breathing out is harder than it sounds. I am working up to a 20 second in/20 second out, but I am already noticing improvement, and less fatigue. Take a moment to look up breathing exercises online, there are several different ones, but this one seems to work best for me. Its worth a try, and won't hurt you. Write back if you discover a breathing program works for you.