Generally, cough will subside after taking medicine. However, beware if the cough you suffered didn't go away. It could be, a prolonged cough is a symptom of serious illness.
It could be TB. It could be also others, such as bronchitis, pneumonia, or bacterial or viral infection. Therefore, it should be checked medically, then we just know.
To distinguish the symptoms of tuberculosis and the usual prolonged cough, it can be considered from the type of phlegm. To differentiate them, tuberculosis is an infection, right? So, there are symptoms of infection, such as yellow or green sputum, fever, and when through the process of röntgen and lab, it was positive.
Meanwhile, in some other serious diseases, prolonged cough may indicate asthma, allergies, respiratory problems and even cancer. The trigger is also the cancer itself, usually throat or lung cancer. That's very possible, especially with the exposure to pollution and cigarettes.
Generally, a prolonged cough will subside if the originator has been resolved. Usually, if the infection is due to bacteria, yes, give antibiotics if necessary. If due to mechanical inflammation, or there's a trigger like dust and smoke, it should be avoided from the exposure.