It most certainly is... I suffer from this myself and have done for many years. Not only are you allergic to onions, but i advise you to stay away from Garlic, Leek, Chive and cellary too, as these are all from the same family.
It sounds like you have an allergy to onion. The onion food allergy is a two different type of reaction like immediate and delayed reaction allergy. In immediate allergy to onions you might experience coughing, vomiting, skin rash and swelling of your face. And in delayed allergy to onions may occur stomach pain and headache. I think,you must avoid to eat onion.