Hi
Welcome to the health care magic and thanks for asking your query here
There are variety of medical conditions which may cause
chronic cough but as your cough did not responded with course of antibiotics and if you have no
fever associated with cough then it is highly possible that you may have
allergic cough which may be caused by any allergen like dust , pollen grains ,even
cold weather and some times some medicines , foods and occupational substances may lead to allergic cough
Try to avoid such allergen which seems to worsen your cough , steam inhalation is a good and it will clear the airway , along with this some Breathing exercises (eg. YOGA) are Also helpful
but if your cough doesn't get better then i would strongly suggest you to see Your
ENT specialist , he may go for all necessary medical investigations to rule out any underlying medical condition including an allergy
i hope it helps
And get well soon