Two of my co-workers have this cough you describe, both on blood pressure medication.
Acid reflux can also cause chronic cough.
The remedy I know works is cayenne and garlic combo. You can make pesto from red cayenne pepper and garlic add a little Sea Salt , olive oil and lemon, it stays good for months without refrigeration, but I do refrigerate mine.
One thing I learned from my visit to India, in the state of Gujarat every home has this pesto on the table and they just take a pinch of it with their meals.
Also we have garlic & cayenne pepper pills now here in the US.