Statistically you’re unlikely to have lasting issues as a result of getting them removed. It’s a very common outpatient procedure.

When you go in, they’ll likely give you nitrous oxide, which will make you relax a little, and they’ll let you sit and breathe it for a few minutes. I’d recommend bringing headphones since some nice music will help.
Then they’ll give you an IV that will make you not worry and likely barely remember what comes next. Basically a big dose of super valium.
Then they’ll give you some pain killers and local anesthetic and remove the teeth.

Your memory and orientation will start to come back in about an hour, by which time hopefully the person who transported you has gotten you home. You will not be able to care for yourself during the intervening time. You will be uncoordinated and of poor judgement.

When you get home it’s best to try to sleep until the meds that the dentist gave you wear off, or just watch TV. Take ibuprofen or Tylenol mostly, but an occasional opioid will help since there is some pain that the antiinflammatories don’t help with as much, although they take care of most of it.
Soft foods for a few days, and no straws.

All in all, you should be back to normal within two weeks, and you’ll get to feel nice and excited to eat something crunchy or chewy.

If you’ve had pain associated with your wisdom teeth, I’d recommend going forward as scheduled. The pain may have gone away temporarily, but it’ll come back.
I let mine go too long, and one of the wisdom teeth cracked open because of pressure on it from another tooth, which also damaged that tooth which was fortunately able to be repaired.
The pain from waiting for outstripped the discomfort of the procedure.