How can I get rid of a sick hangover in a couple hours?

You can't generally. Hangovers last how long they last. There are dozens, if not hundreds, of hangover "cures," and when you see something where there are that many "solutions," it is usually because none of them work that well. Hangovers come from drinking too much, and the "cure" is not to drink that much. To some extent, "clear" alcohol causes fewer hangovers than "colored" ones. Latest cure- warm Sprite. Cut down!