Hello Welcome in H.C.M. I have gone through your query regarding productive cough with grey sputum after 3 days of hospitalization for hysterectomy operation. This productive cough is indicative of respiratory tract infection and it is not concern with your operation (hysterectomy), except if your operation is done under general anesthesia with endotracheal intubation. Because in general anesthesia with endotracheal intubation there are chances of infection to respiratory system. Beside above there are so many factors concern with air & water pollution and infection by edibles may infect respiratory system. Lastly I would like to say that every infection has got it s incubation period (time interval between entry of infective organism and development of symptoms) so it may be possible that you might have infected early and symptoms appear later after 3 days of hospitalization. All above will be clear only after examination and isolation of causative agent and their pathogenic nature. Regards.