This is not medical advice, and could even be wrong. However, I had a friend with with the same problem and he did have asthma. The thing that helped him the m

This is not medical advice, and could even be wrong. However, I had a friend with with the same problem and he did have asthma. The thing that helped him the most was dialling it back completely. Run 1km, does that make you cough? Run 0.5km. Once you get a distance where you don't cough, run it for a week or so, then increment by another 0.5km. If you start coughing, reduce it again.