Is wheat sensitivity the same thing as celiac disease?

Not exactly: Celiac disease is an immune mediated IgA adverse reaction to gluten (a protein in many grains including wheat) typically leading to GI symptoms. Wheat allergy is an IgE mediated reaction reaction that can be very severe leading to anaphylaxis that can include GI symptoms. An allergist and GI specialist can assist patients who have suspicion for celiac disease and/or adverse reactions to wheat.