Salicylate sensitivity is any adverse effect that occurs when a usual amount of salicylate is ingested. People with salicylate intolerance are unable to consume a normal amount of salicylate without adverse effects.

The most common symptoms of salicylate intolerance are:

Stomach discomfort, diarrhea, or constipation

Itchy skin, hives (also known as urticaria, is a kind of skin rash with red, raised, itchy bumps), skin rash,

Asthma and breathing difficulties

Headaches and others

There is no laboratory test for salicylate sensitivity.  Typically testing is done by an "elimination and challenge diet.

An elimination diet avoids salicylate-rich food. Maybe after 2 to 4 weeks, you start with a challenging diet.

During the provocative challenge, the person takes incrementally higher doses of salicylates, usually aspirin, until symptoms appear.

Suppose the elimination diet is able to eliminate the salicylate-associated symptoms and the challenge diet is able to trigger the symptoms. In that case, you can learn which type of food might be inconvenient for your digestive system. 

A dietician or gastroenterologist can guide you regarding the diet plan.