If you have a morphine allergy can you take oxycodone for severe pain management?

No, you cannot. since hydromorphone is morphine with an extra oxygen molecule that allows it to pass through the blood brain barrier faster (much like heroin is actually morphine also but with an extra acetyl molecule), you will still have the same allergic reaction. try Oxycodone (percocet) or Hydrocodone (Vicodin) instead.