The diagnosis of an allergy to aspirin or ibuprofen is usually a clinical one. In other words, it is based on symptoms, which are usually easy to spot.
While many allergies have definitive tests such as skin tests or blood tests that can be used to detect their presence, no such tests exist for NSAID allergies. However, allergy specialists may sometimes ask patients to do an oral challenge, especially if there is good reason to think that the patient may not actually be allergic to NSAIDs. Needless to say, an oral challenge should only be performed in a hospital or clinic where the patient can be observed and quickly treated in the event of a severe allergic reaction.