Technically, you are not allowed to take a full-time teaching position (that would require an E2 visa). If you can find a school or hagwon that will take you on, you may be able to get an E2 at the nearest embassy (Fukuoka, Japan) - but they generally require an interview in your home country.
If you don't have any other qualifications, your opportunities for work are extremely limited. If you speak good Korean you may be able to get short -term work, but this would be for "cheap" Korean wages (which everyone else in Korea seems to get by on). You could try the Western bars or restaurants in Itaewon, or just find a hagwon that's willing to ignore the rules (though you risk deportation).
If you just need to survive, there are volunteer programmes that provide food and board. WWOOF springs to mind, but they work you hard over here so you'd only be able to see your gf on weekends.