Yes I Have A Cough For Several Months Now. I

Yes I have a cough for several months now. I have been to the doctor twice. First time he gave me an antibiotic because he heard something in my lungs which helped but I still have the cough. Second visit we changed my allergy meds. This did not help either. I do have nasal drip from allergies but when I breath in I feel it in my chest and cough. Should I see a specialist and if so what kind. Thanks.