Can each of my meds be tested on me somehow to find out which, if any, are causing my hives/ allergic reactions?

Hives: No. Hives can be due to many things including meds, foods, infections, autoimmune, irritation, underlying disorders, etc... It is also not possible to simply believe it is one of your medications. People always want a "cause and effect" but rarely is there one. An allergist can help.

Medication allergy: Unfortunately, there are very few tests for confirming drug allergy. While there is a skin test for penicillin and local anesthetics, its not available for others. Only by stopping a medication and monitoring for resolution of hives will suggest that as the cause. An allergist can work to find the cause of hives.

See a dermatologist: Some meds are common causes of hives, some are not. Very few tests are useful for this. Very often the cause is never found. Aspirin and ace inhibitors are the most common causes of hives. But any med might be a cause. Your dr might need to carefully try you off one or more meds. Meanwhile see a dermatologist for diagnosis & management. Some kinds of hives are not allergies.