The term atelectasis signifies collapse of lung tissue. It can range from collapse of a small portion of lung to collapse of the entire lung. The term compressive atelectasis refers to the circumstance when the collapse occurs in response to physical compression from an adjacent organ, such as an enlarged heart or by hyper-expanded lung next to the compressed lung, or more commonly by fluid or air in the pleural space. The implication is that were the collapsed portion of lung not impinged upon, it would be normally expanded.
In your case, the question is: what is causing collapse of the atelectatic lung? This is a question you should ask of your doctor and/or the radiologist.
If the cough you have had for the last 3 months is a new onset cough, at age 47, there is a possibility that the cough could be related to the atelectasis, more specifically to the cause of the atelectasis, as could your “shortness of breath with activity.” In any event the cough being both new-onset and now chronic warrants further investigation. Your concern is appropriate.
If your doctor does not respond to your concern, you should request consultation with a lung specialist, also known as a pulmonologist.