I cough a lot too, all of what you are experiencing I to experience the same. I do, end up throwing up this happens at night mostly. I figure with time it will go away.
My mother smoked for years and she quit in 2000 and she still is coughing at times.
I guess it just takes time for our bodies and our lungs to get that stuff out. We don't really realize what we have done until we decide to correct it... I am very proud of you for quitting