Yes, you can be allergic on various food, and if all the major culprits are excluded by tests, you should go through the extended list of food additives or preservatives because those are the most suspicious things if you suffer some sort of the food reaction.
Usually those can easily be some artificial, synthetic chemicals added to the food to improve shelf time or durability during transportation, but sometimes it can be intolerance of specific natural chemicals.
People with adverse reactions to shelf food or condiments, should strictly avoid that sort of the food and eat organic.