Oat allergy is different from celiac disease. Celiac is all about gluten intolerance and oats don't always have gluten in them. When people develop this allergy they generally suffer through some common symptoms like running nose, cough, sneezing, nausea, sore eye, headache etc. Anaphylactic response is the most common and dangerous reaction to the oat allergy. An anaphylactic shock is a combination of near fatal allergy symptoms, such as severe skin swelling and irritation, irritation of the digestive organs, palpitation and difficulty breathing. The ELISA test measures the amount of allergen-specific antibodies in your blood.