you are probably suffering from naso bronchial allergy
It is a condition which effects a lot of people and results in persistent cough
, more so with the change of the season.Basically it is the result of overproduction of allergy antibody i.e Ig E in the body.
Lot of research is going on in for the role of vitamin C
and vitamin E
to raise the immunity of the person,although nothing conclusive has come up.
You can try Vitamin E for few weeks, it may help a bit, but remember it is not a water soluble vitamin so can accumulate in the body if taken for long periods to cause side effects.
Please get the basic investigations done to see if there is a modifiable cause to your problem.
Hope it helps.