Why does hydrocodone make me itch?

Hard to say: Because this is often an "idiosyncratic" reaction to opioids - one with great individual variation, which may be genetic in nature. Opioids cause release of histamine in most people, but it is usually mild; however, in some it is more severe and causes itching, and even hives, flushing and GI problems. Oxycodone does this less, as do some of the synthetic drugs like fentanyl. Talk to your doctor.