Suggest Treatment For Post Nasal Drip

Hi, I don't run often but am starting to train for Marine Corps boot camp. I'm not overweight, I eat healthy, don't smoke, lift weights 3 times a week, and walk 6+ miles every day.

Now after I run about 1.5 miles, I seem to wheeze. I believe I have post nasal drip because I always seem to have excess mucus in the back of my throat, so I'm wondering if this might cause it. The symptoms seem to dissipate after 10-15 minutes of rest after running. I experience no chest tightness either.

Could this be caused by post nasal drip or not being used to running, or does it have to be asthma?