Hi, you might know that there is commonly a dry cough from the class of hypertension drugs called ACE Inhibitors. A cough from losartan (which is not an ACEI, but an ARB class) is much less common; but that still seems to be the best suspect. The 'A' in each class stands for angiotensin, so the way that they work is related.
The metoprolol (from the beta blocker class) is also a possible cause, but less likely.
But then again, you'd probably expect the cough to have started sooner than months after beginning the meds. So maybe it's a virus. Or if there is green sputum, you need an antibiotic for a bacterial lung infection. Red means bleeding.
Ugh, I hate a lingering cough. Couple of things come to mind. First, coughs can last a long time. Once the airway and bronchial tubes get irritated, they take a while to get better. So the least little thing will cause a coughing jag (exertion, changing position to lay down, etc.). It can happen that it takes 2 months to get over a cough because of this. But there are other things to consider. You can get a type of asthma related to having been sick and this airway irritation. There is asthmatic bronchitis. An inhaler may help with this if it is the case.
Another possibility and I don't mean to alarm you but having a cough that won't go away has been associated with a cardiac issue.
So, bottom line, you need to see your doctor.
I listened to a doctor's radio program and all the doctors on the program were in agreement that honey (especially darker honey) works as well as any over the counter cough suppressant if not better. Have you tried that?