Is it normal to have a cough last 3 months or is something seriously wrong with me?

I have a coughing problem. I'm 21 yrs old and whenever I get sick, the coughing lasts weeks or months. Last year, I caught the flu and the cough lasted for 3 months. I took every medication you can think of and nothing work, it just went away on its own. At the time, the doctor told me that the virus was gone but my lungs are taking longer than usual to heal for some reason. It's happening to be again, I went to Los Angeles last month, caught a virus and I'm still coughing. Its been 4 weeks now! Why is his happening to me? I can't take this coughing anymore. I don't smoke but my parents smoke a lot, not sure if that's a factor,