Hello, 
Thanks for the query to H.C.M. Forum.
I would come up with these possibilities for this type of 
chronic cough, these includes.
1 .Allergic 
bronchitis ( asthmatic ) , usually in this type of cough allergy is responsible .Diagnosis can be confirmed by physical as well clinical examination by a physician . Usually this type of cough is  stimulated by mite, dust, cotton fiber, hay , cold , sudden rise & fall of temperature , pollen, mold.
Avoidance of these provides relies.
Sudden exercise increase demand of oxygen , but due to 
bronchoconstriction there develops cough.
2 
Throat infection is the next reason. Diagnosis can be  confirmed by swab from the throat.
3 
Eosinophilia may be possible next reason.Diagnosis can be confirmed by blood examination for eosinophils count.
In my opinion as all tests are normal so ,consult a physician and get his treatment for asthmatic allergic bronchitis. 
Good luck.
 DR. Het