When your body sees wheat as an invador and attacks it--not your body. Symptons of wheat allergy could be eczema, sneezing, increased acne. If you have a very serious allergy, you might have an anaphylactic reaction in which your throat would swell up to the point where you could no longer breath.
Dairy-free is for you:
Gluten-free diet just means strict avoidance of wheat, rye, barley (and, currently, oats), even in tiny amounts. This has come to represent the celiac diet.
Vegetarians do not eat meat, fish, or poultry. Vegans, in addition to being vegetarian, do not use other animal products and by-products such as eggs, dairy products, honey, leather, fur, silk, wool, cosmetics, and soaps derived from animal products. In other words, nothing that has a face or comes from anything with a face