Gustatory rhinorrhea is the name of the medical condition that gives you a runny nose when you eat. Gustatory rhinorrhea is thought to be a reaction to the temperature of the food or reflex to chewing. The treatment is to take antihistamines one hour before eating. You may have to try different ones to find one that works best for you.
There is a medical term for a runny nose while eating, it is called Gustatory Rhinorrhea and is embarrassing to those who have it. It is usually just a simple reaction to the temperature of the food, either hot or cold.