Having been conscious for the removal of baby teeth taken out that were pretty much ready to go anyway and barely had any roots, I can say that you are about to have one of the shittier days of your life. The problem isn't so much pain, as the sensations. Cracking, grinding, pressure. It sucks a lot. Wasn't terribly painful afterwards like my wisdoms, but the experience was highly unpleasant.
Get knocked out. You won't remember large parts of the rest of the day, but it's way preferable. Waking up in that kind of pain is bad enough, but having to be conscious through an hour or more of it? Fuck that shit.