What antibiotics is good for a prolonged coughing in adults?

Most coughs are caused by a viral infection (larynx, bronchi, trachea) and therefore antibiotics do not treat such infections, on the other hand there are coughs which are caused by a bacterial infection like streptococcus pneumonia.
It is important you see a Dr. in order to determine if you have a viral or bacterial infection in order to follow the correct course of treatment.