Allergic rhinitis: Medical term for hay fever, an allergic reaction that mimics a chronic cold. Symptoms include nasal congestion, a clear runny nose, sneezing, nose and eye itching, and tearing of the eyes. Postnasal dripping of clear mucus frequently causes a cough, loss of smell is common, and occasionally loss of taste. Nosebleeds may occur. Also known as June cold and summer cold.