Cough for nearly 3 months not improving? ? mother had a history of throat cancer.

Chronic Cough: Of course, a chronic cough can be due to copd, bronchitis or emphysema. Asthma can also cause this. You didn't mention your age, but if you are "young, " COPD is unlikely, unless you are one of those rare people with alpha1-anti trypsin deficiency. Throat cancer is very unlikely to cause a chronic cough and not hoarseness. I would suggest a consult with a pulmonary specialist if it doesn't clear.

Time to see doctor: Three months is a long time for an unresolved cough. Please see your doctor for an evaluation. It is not feasible to provide a meaningful opinion without further history, physcial examination, may be imaging and lab studies.