Various modern medicines are quite different from one another and hence no one can be allergic to all allopathic drugs. Your wife is allergic to NSAIDs (Non-Steroidal Anti-Inflammatory Drugs), which have a similar mode of action. Even paracetamol has anti-inflammatory activity though much less than diclofenac, mefenamic acid, meloxicam etc. She must not take these medicines.
One can test the allergic reaction by giving a very small dose of a medicine such as one-tenth or even less of the usual dose to see if the patient is allergic.
Any consultant physician such as the one has done MD in medicine should be able to help you out.