If someone gets sick from taking hydrocodone will they also get sick if they take oxycodone?

You must define sick: If it is a true allergic response - hives, wheezing, skin rash - you may respond to other opiates similarly. If it is related to histamine-release (which is prominent with hydrocodone and less so with oxycodone) - which can cause itching, flushing, GI symptoms - you may not get it with oxycodone. The best answers would be from your prescriber and/or your pharmacist. Please ask them for advice.