I think an allergy can show up in different ways in different people. My daughter is also allergic but doesn't get a rash. She has stomach problems and asthma like symptoms.
Her doctor told me that ibuprofen can trigger an asthma attack. My daughter doesn't have asthma normally but develops it as an allergy symptom. Ibuprofen also gives her nausea and stomach cramps. She is not allowed to have this pain reliever ever again, the information has been added to her medical profile.