Senior year in high school, my tonsils got very swollen and infected. They gave me a VERY hard time through my college auditions. A year later, they did not fare well in freshman year. They were constantly getting infected, they were quite swollen all the time and they were often very painful. I got them removed first day back after my freshman year. Needless to say it was the worst pain I've ever been in. You should seriously consider the possibility of living with them. If you feel there is no other alternative, go ahead. But I don't say that in defense of your bassoon playing--- life is long, there's plenty of time to relearn how to play bassoon... especially if you have a summer off to do so. You will not recover quickly. As an adult the recovery period is of course longer. I tried to play at three weeks and the pressure caused hemorrhages.
There would be small pockets in the sides of your mouth that will both leak air and catch food.. quite annoying for a while, but they eventually fill in a little and your mouth reaches a new equilibrium.
Please listen to what everyone is saying... the recovery process is not easy at all. It is EXTREMELY painful and will render you incapable of talking, eating, swallowing, barely breathing (not to mention sleeping) for two weeks.
All in all I think my procedure was a good decision. I haven't gotten sick since, and my playing improved exponentially after I recovered and reapproached the instrument. After all, nothing like a technique and embochure re-set with PROPER form when you can really pay attention to the small details. Take the reapproach to the instrument as a fresh start, a way to start good habits from the very beginning to solidify your development.