Brief Answer:
Get the advised investigations done
Detailed Answer:
Hi Ma'am,
Thanks for your query.
Your symptoms are suggestive of either, Chronic 
sinus problem; 
allergy (perhaps pets, worms infestation  or, microfilarial infection); early asthma; Chronic Bronchitis; or, drug-induced (Cressar- though less likely).
Get blood checkup done including, CBC, 
Eosinophil count, AEC and microfilaria; Pulmonary functions test and chest X-ray. These test-reports will identify the real cause of your 
chronic cough.
Give a 2-weeks' trial of anti-allergic drugs : Levoceterizine + Montelukast; 
Codeine cough syrup and, avoidance of contact with pets. See the response. Improvement in symptoms will confirm allergy/early asthma.
	
Consult your doctor and apprise him of my opinion. I am certain that he will agree  with me;  order required tests, and- based on the reports-  will arrive at a certain diagnosis and  prescribe suitable treatment as advised.
Hope I have addressed to your concerns to your complete satisfaction and you find my response helpful and informative. I will be happy to answer further queries, if any.
Fond regards and have a nice day,
Col (Dr.) Rakesh Karanwal