Your symptoms suggest a post-viral cough or post-nasal drip, which is common after respiratory congestion. The itchiness is likely mild irritation from coughing or lingering inflammation. To soothe it, drink plenty of warm fluids, use throat lozenges, and do warm salt-water gargles twice daily. An over-the-counter antihistamine or cough suppressant may help reduce the urge to cough. If the cough persists for another week, worsens, or you develop a fever or difficulty swallowing, please consult an ENT specialist for further evaluation.