Celiac Disease (Gluten Intolerance) and Gluten Sensitivity involve immune system reactions to food that are autoimmune in nature, not type 1 classic IgE mediated allergies. Therefore food "intolerance" can be more than just an enzyme deficiency.
There can be other immune reactions to foods that do not make use of IgE antibodies also. For example, Sulfite Preservatives can trigger histamine release and mast cell degranulation without going through IgE antibodies to do that - and the reaction can be every bit as dangerous as "true" food allergies. I know, because I've had Anaphylaxis from Sulfites. Sulfites are in a lot of processed and packed foods (such as canned foods, wine, foods with vinegar such as salad dressings, bottled lemon juice, etc.). And I personally believe that a lot of other things such as food colorings, etc., can trigger allergy or allergy-like reactivity as well.
Please see an Allergist, and if that turns up nothing (many allergy tests can have false negatives), go see a Naturopathic Physician for help doing an elimination diet.
Also, 1 week may not be enough time to see if a particular substance is causing trouble. The minimum recommended time I've seen is 2 weeks, but in the case of gluten or casein (can take 3 weeks just to get the reaction, not to mention how long after that it would take for the symptoms of the reaction to subside), it takes at least 6 weeks for the protein to leave the gastrointestinal tract and up to 1 year for it to leave the brain.
Anxiety as a reaction strongly suggests gluten, but could be something else. Ask for the gluten antibody test (Celiac Panel), and make sure they test Total IgA, anti-Gliadin IgA, anti-Gliadin IgG, and anti-Tissue Transglutaminase IgA. Prometheus has a pretty good Celiac Panel, so do some other labs.
Gluten & Sulfite Sensitivity, Multiple Food & Inhalant & Medication Allergies, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD (Lupus?), Osteoporosis, Anemia, Very Low Lymphocyte Counts (T-Cells & B-Cells), malabsorption/malnutrition, etc.
Meds: Pulmicort, Injectable Vitamin B12, Herbs, Nutritional Supplements, Essential Oils, Homeopathy.