Have occasional mild hives that get worse with ibuprofen. Don't know if this means I have ibuprofen allergy. If so, am I allergic to aspirin too?

Probably. There is cross reactivity between aspirin and NSAIDs as ibuprofen and the like, but whether you're truly allergic to this class of medicines is yet to be sure of, visit an allergist, in the interim avoid NSAIDS and aspirin, use acetaminophen for pain and fever till sorted out.