Coughing for 1 month, not resolved by meds. thick yellowish green sputum sometimes got brown spot. no fever no pain only the cough. throat felt itchy?

Cough?: There are many reasons for a cough, many of which are non-infectious and do not require antibiotics. Some are even caused by medicines. You have to at a minimum have a virtual consult, but preferably see a live doc who will get a full history, a thorough physical exam, maybe some lab tests and come up with a diagnosis and treatment plan for you. Good luck!