that entirely depends on how your teeth are coming out and how they're formed and how well your dentist knows what he's doing.
some people have ridiculous wisdom teeth that can be pulled out like they're baby teeth.
others
others seem to almost be stuck to the bone and another tooth and are hard to remove.
are your wisdom teeth even showing? if yes, how much? because if they're only partially out, you're probably end up getting them removed surgically, which is a real pain. to do that, they cut really deep and cuts heal bad. theres also a bigger chance for infections which prolong the healing time. surgery also causes more swelling afterwards.
on the pro side, you're usually out cold during the removal and they often just take all 4 at once while they're in there.
but depending on how well things go, you're gonna feel that for a few weeks if you're unlucky/have complications.
if they're all out like the rest of your teeth, it can be easy or hard, depending on how they're formed and if they get stuck under another tooth. but after a normal pull, you can pretty much go to school right afterwards (but you dont have too, you can usually get a slip because you feel whoozy afterwards or something. at least you can stay away from sport, the strain could end up cause bleeds.
and unless the dentist is really bad, things will heal up rather fast, as long as you keep it clean (salt water against infections, no milk products, no smoking etc)
the pain in general is often ok during the removal, that is, if you get anesthetized. i got like two injections (i had to ask and pay for the second one, its worth it i believe) and only felt the pressure on the jawbone while the dentist tried to strongarm the tooth out. that felt scary cause i dont have the strongest bones, but not painful.
got a bunch of pills for the next few days and after a week it was mostly back to normal.
anyways, if your tooth is infected, they cant remove it right away anyways, you'll have to take a weeks worth of antibiotics (dont just any ones, dentists use a special brand thats stronger on the tooth related bacteria) and maybe a drainage before they can think about removing it, cause otherwise no injection in the world will stop pain and things get infected afterwards for sure.
so go to the dentist soon, so he can check that up and start the treatment soon.
*all that is how its usually handled in germany, under Statutory Health Insurance - apart from the second injection of painkillers, i paid nothing for the removal of my wisdom teeth. it may be different/more expensive in the us though. maybe regulations are different and they just go for the tooth no matter the infection level.
as a tip on how to cope with swollen gums, i usually used one of those cotton rolls that dentists use
http://www.zahnarzt-praxis-halle.de/wp-content/uploads/praxisfotos/watte.JPG
alternatively, make something similar out of kitchen roll.
make them wet and use them to push away flesh from between your teeth and wedge them between teeth and cheek. its hard to explain but the important thing is to get stuff away from your teeth so you dont bite on it all the time.
it may feel weird and uncomfortable for a while and it looks really dumb, but it helps, biting only causes more swelling and pain which in turn makes everything take longer to heal