The coughing fits that you have while you are running are peculiar, especially since you don't smoke. This makes me wonder if you have a mild case of exercise induced asthma
. Asthma is known to cause shortness of breath, but that is not the only symptom. Some people experience more of a cough with their asthma than shortness of breath. We call this cough variant asthma, and it gets treated in the same way as any other case of asthma. Some people with very mild asthma only experience symptoms when they are exercising. The only way to know for sure is if you try a asthma medication prior to a run and see if that stops your coughing. If it does, that will be your diagnosis.
I suggest that you schedule an appointment with your primary care physician
. He or she can ask you more questions regarding your symptoms and perform a thorough physical exam. Your doctor
may want to perform more intensive testing including pulmonary function testing. This is a test to see if your lung function is consistent with an asthma diagnosis. Alternatively, your doctor may want to just prescribe you an inhaler to try before your runs. Good luck.