Hello and hope you are doing well.
There is an entity called exercise induced Asthma, here as the person starts exercise, the changes in the environmental air breathed in trigger an attack of asthma, causing cough and breathlessness. Have yourself evaluated for the same. This can be detected by a spirometry test.
Hope this helped and do keep us posted.
Can you describe what you mean by difficult to breath?
I have described my nasal congestion (easily treated with a decongestant nose spray, unfortunately this doesn't cure my problem) as difficult to breath. I can still breath through my mouth so maybe it is a breathing difficulty. I mention as an example of why a better description from you may result in some connection with readers of your post.
My condition is particularly a problem when sleeping, not so much when I am up and about. I have a prescription nose spray that helps a little but not as well as the don't use continuously over-the-counter sprays.
I think mine may be an undiagnosed allergy. Not sure and I have discussed it with my primary care doctor and with his nurse practitioner - both think the prescription nose spray is the answer - I don't recall what it is called, I can look if your problem is similar.
Another symptom I have from the nasal congestion is "dry mouth" caused by breathing through my mouth.