Thanks for your query.
Dry irritating cough has several reasons including infections, acidity, posterior nasal drip, post viral cough
where cough persists after acute viral respiratory tract
infections, as side effect of certain blood pressure medications etc..
If you have taken antibiotics and cough is not relieving , better meet a chest specialist, who may advise chest xray, pulmonary function test, sputum examination and if needed CT scan