I had a cough for awhile around when I got married and it was annoying. They told me they treat by exclusion with it, so I was on AR meds for awhile and those didn't help, then they did a test and said I was slightly asthmatic and gave me an inhaler which didn't do anything but make my jumpy. I think they also said I had slight bronchitis.
I think it was all bull, though, and it went away on it's own. You could try some tea tree oil in a bath or on a washcloth while you shower and see if it helps.