I can relate to your problem. I'm also 22 and have been on pain meds (bulging cervical discs and postural crap) for a year and a half. My doctor is actually fairly liberal about giving me pain meds, even though docs will rarely put people our age on opiates.
I guess my question for you, is why will you ONLY consider Vicodin? That will likely be what raises the red flag. Obviously you're not some hopeless addict if you've had 3 surgeries, but doctors have to be extremely careful and discerning about writing painkiller prescriptions. Unfortunately, even if you like Vicodin for pain now, eventually it'll wear off... like they all do.
I'd say the best way to go about it is to go to your doctor and simply say "I'm in pain, it's affecting my life detrimentally, what we are currently doing (as to opposed to "What I'm currently TAKING") is not effective enough to allow me to live my life, what can we do to change that?" Then allow him to talk... he will probably name a few things (patches, OTC, etc.) After LISTENING to the options, explain why or why not you think they would be effective. If you go in with the mindset that your doctor is there to help you, not to prevent you from feeling better, you will be better off.
Good luck... and that really sucks about your back. You can read my story in this forum if you want as well.