How badly will this hurt?!

Dont be scared, I got all of mine removed at once and they were impacted like yours (minus the infection) and it doesnt hurt. The gas has you out of it and you wont feel anything. The only bad part about is that your cheeks swell up and you look like a chipmunk and you wont be able to open your mouth wide enough to fit anything but a small spoon for a couple days. Just make sure you keep the sockets clean so you dont get an infection.

I found that the most painful part of the procedure for me was the injection of the local anesthetic, beyond that, you just feel a lot of tugging and you'll eventually hear a crack, which is the tooth coming out.
It doesn't really hurt, but the pulling can get mildly uncomfortable at times, mostly because your face is being tugged around!! Its pretty annoying actually, but not painful!

I've had 4 teeth removed so i could fit braces.

Just so you know...
Getting any bottom teeth out hurts more than top teeth. Ask for the top first.
But no, dont worry, It will hurt a little, and afterwards it will bleed abit. So yeah, it might hurt, just a little. But seriously, I've had it done, itshould be fine after a day or two xD

Experience

The gas will knock you out, so you wont feel them being pulled.
You may need to take pain killers afterwards for any discomfort, just keep clean do as the dentist says.

When you're on gas you still feel something but you just don't care. :)

Experience.