Have you had your sinuses checked?
Any problem with heartburn or indigestion?
Is this a completely dry cough?
OK--all I can do here Margaret is give you my thoughts--let me know if you need more information.
I would get a ct scan of your sinuses to look for a chronic infection there since post-nasal drip from that could be the problem
But much more likely is silent gastric acid reflux--no indigestion or heartburn, but the acid reflux is aspirated into the lungs causing a chemical bronchitis.
Were I your doctor I'd get the scan and give you a two week course of either Prilosec or Nexium to see if that clears this up.