Believe it or not, smoking can diminish the cough reflex. In effect, the smoke deadens the cough nerve endings. Then, with smoking cessation, the cough nerve endings in the throat become more sensitive. The combination of increased cough and improvement in mucus clearance, results in a bad cough, often with very discolored phlegm. This can last for 3 months or more until your phlegm starts to diminish.
Your doctor might want to give you a trial of an inhaled steroid. This could result in less inflammation of your bronchial tubes, with less phlegm and less cough, as it does with asthma. The cough and wheeze are unpredictable. They may or may not go away, unless treated with an inhaled steroid.
From what you describe, you are miserable, what with the cough, wheeze, phlegm stuck in your throat and shortness of breath. But the odds that you will gradually get rid of these symptoms are high, in your favor. You may be tempted to resume smoking but don't succumb to the temptation. Stopping smoking was a very good decision and, at nearly 2 months, you are almost over the hardest part.
Good luck