The most common causes of otherwise unexplained chronic cough are postnasal drip, gastroesophageal reflux (GERD), and asthma. For you, the most likely cause would be chronic bronchitis from smoking. However that should not be assumed to be the cause unless you stop smoking and the cough stops.
Suppression of the cough is surely satisfying. As you have noted this gives no information whatsoever about the cause, be it serious or not. Having had this cough for months, you should be seen by a lung specialist.
An ongoing cough can also be a side effect of a group of medicines used to treat high blood pressure called angiotensin converting enzyme (ACE) inhibitors. Neither of the 2 medicines that you are taking are an ACE inhibitor.