Could be either, could even be egg or something else entirely. Would advise to invest in blood tests. With mine, the first time they drew a vial of blood and tested it for signs of allergiec reactions (results can only say yes or no). When it was yes, went to have skin prick test. They just make a bunch of tiny holes, rub different allergens into them and measure the swelling after 30 minutes and compare it with a chart.

Could also be a yeast allergy, my dad battles with some breads because of the yeast used.

I agree with Lady Catherine. Your PCP can do an in office blood culture to see if you have celiac disease. You would need to go to an allergist to test for the wheat allergy. Gluten intolerance ( Celiac Disease ) is the bodies in ability to break down the proteins and it affects your GI more lite IBS, or Ulcerative Colitis. A Wheat Allergy would make you have a rash. I am allergic to Wheat but I have EOE which causes my esophagus to close up around the bread I can still breathe but I feel choked. If I was to be in contact with raw wheat I would break out in rash and inhalation of Flour causes Allergic Rhinitis. I hope this helps.

I would go to an allergy specialest if you have one in your area. Its important to get a diagnosis so that when your getting treatment you can refer them to that dr.
I agree to cut glutin out of your diet for a month. If you find relief then you know. Glutin is in a lot of our every day things like food additives and medications. If youve been feeling bad (including depression and anxiety) you will start to feel much better! I did! It was like a black cloud was lifted and i felt happy again! I wish you the best on eliminating glutin. Its a difficult thing but so worth it!!

It could be wheat/gluten. The best would be to avoid it or try gluten free bread.
Do you get the same reaction eating pasta or other wheat/gluten products.
If not it might be something else.

Best would be exclude it.