Obviously, see your doctor or a qualified medical professional. But as a former smoker, I'd say absolutely that your productive cough is due to smoking. Your bronchi are producing extra mucous cells to create more mucous to help remove the particulates in the smoke from your lungs, working with the cilia. That's what produces the phlegm.
If you do not quit, over time the cilia will disappear and eventually the mucous will plug the smallest air passages. That's called COPD (chronic obstructive pulmonary disease). You'll inhale but the little air sacs will eventually lose elasticity and not be able to expel the air. That is called emphysema. They become enlarged and the walls between them break down. Then, the carbon dioxide in your blood builds up and at some point you'll need supplemental oxygen. Before that point you'll see gradually increasing shortness of breath which worsens with exercise. That takes several years but never gets better, only worse.
The point is, there is no good outcome for you if you continue to smoke. The earlier one quits the less permanent damage to the lungs. No, your lungs do not heal 100%. The air sacs that have become enlarged and merged with other sacs are like that until you die. The sooner you quit yes, salvageable lung tissue will improve function.
I found nicotine lozenges very helpful for quitting. Heck, even if you become addicted to those at least you're not inhaling smoke. :)
Not telling you what to do. I think you know what you need to do. Once you get over the hurdle of quitting smoking it's great! I never even think about it anymore.
