Why do I have a terrible back itch after drinking alcohol?

Hard to say. Alcohol causes flushing, in part by release of histamine and in part because of direct vascular effects. In most people it involves the face and neck, but others get flushing (together with itching) of the back, chest or the entire body. It usually means you have either a variant enzyme that metabolizes acetaldehyde into acetic acid and water. This is most common in Asians & Native Americans.