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To be clear: A wheat allergy is not the same as having celiac disease. If you're allergic to wheat, you suffer from an immune response to a protein in wheat and wheat alone. Celiacs, on the other hand, react to gluten, which can be found in rye, barley, and some oats, in addition to wheat. The allergy often affects children and is usually outgrown by age three. About 20 percent of children with wheat allergies have been found to be allergic to other grains.