What Causes Persistent Cough After Suffering From Flu?

I've recently had the flu. Well exactly a month ago. I still have the cough that doesn't seem to want to go away. It is productive all day where usually most is first thing in the morning. The sputum is thick and white with dark brown specks in it. I was at one point coughing up blood with the severe cough associated with the flu but the fact that it continues to linger and it tinged with old blood concerns me. I am a smoker but have never been faced with a scenario quite like this. Do you have any answers?