Hi welcome to health care magic.... Here you are having cough again.... You have taken full course of antibiotic for URTI.... So now it is better to consult pulmonologist for examination and auscultation ... Here chest x ray should be done (as cough more than 3 to 4 week evaluated through x ray )... It might reveal chronic bronchitis or any restrictive disease .... If needed spirometry needs to be done to assess severity and accordingly management ... Sputum cytology examination and culture will also be beneficial for planning further treatment ... If no significant cause detected than no need for worry .... Take turmeric powder in hot milk daily as home remedy . Advise : consult pulmonologist ... Take care