I know exactly how you feel, even if you are eating gluten-free bread.
Unfortunately, most if not all gluten free breads (like most other breads) contain ferrous fumarate to boost their iron concentration. But, unfortunately, the ferrous ion can undergo the Fenton reaction in which the hydrogen peroxide formed naturally in our bodies is converted to the very damaging hydroxyl free radical.
This will make holes in the membranes of the gut lining, which can let all sorts of toxins through, including gluten. So, if you were just intolerant to gluten, if you eat this iron fortified bread it will increase your risk of becoming a full blown coeliac.
My advice would be to avoid all foods supplemented with ferrous fumarate (including gluten free bread) and concentrate on foods that are naturally free of gluten and do not themselves contain inorganic iron.
Red meat would be a good choice, where the iron is firmly bound to the heme in its myoglobin.
Fermented foods such as soy-based yogurt and tempeh are also rich in organic iron, and may be more acceptable if you are a vegetarian or vegan.