Does the mouth wash they give you after having your wisdom teeth removed burn/cause pain. It's 0.12% of medicine I can't remember the name as of now?

Chlorhexidine. The mouthwash you were likely given is 0.12% Chlorhexidine and goes by the names of perioguard or perished. It can cause a little burning due to its alcohol content especially is you rinse too aggressively or for too long of time. Think of how listerine burns your gums when you rinse with it. The keys are to rinse gently for about 30 seconds two times per day (unless your doctor said differently)
Chlorhexidine 0.12% There is evidence that rinsing with chlorhexidine 0.12% provides a benefit in preventing dry socket. Chlorhexidine rinse can affect individual people in different ways. Burning sensation on the soft tissue may be a side effect that is associated with this medicine.