How long does it take to recover completely after having wisdom tooth extraction it's been 3 weeks and i still need to take painkillers twice a day.

Too long: This really varies widely depending on many variables including invasiveness of the surgery, your medical status, individual variation in perception of pain, surgical complications, etc. After 3 weeks, you should return to the surgeon for an assessment of why there is still significant pain.

Please see surgeon: Although no 2 people respond the same way, 3 weeks is much longer than should be. Please call your oral surgical specialist for an appointment to have him/her check and do what is necessary to help you feel better. Don't hesitate to call, the surgeon wants to help your resolve your problem.