Hi, Cough developing after an upper respiratory infection like sinusitis can suggest bronchitis, especially if the cough persists beyond 5-7 days. Here there can be a gradual increase in amount and colour of sputum (initial white and later yellow) for few days, then gradually subsiding. If there is no fever, breathing difficulty or fast breathing, this needs only supportive measures with antihistamine (like tab levocetirizine 5mg at night) and cough remedies available OTC for few days. Otherwise, this may need antibiotic therapy, for which your doctor will guide you. Hope I have answered your question. Let me know if I can assist you further. Regards, Dr. Muhammed Aslam T. K., Pediatrician