How normal is it to have pain 3 weeks after wisdom tooth extraction?

I got ask my wisdom teeth removed 3 weeks ago. I took the antibiotics and pain meds afterwards. The sutures have dissolved on one side of my mouth. I have a hole there now. My lower extraction sites hurt. Is this normal?

No, pain should subside after around 1 week and be under control with pain relief. If the sutures are still in the sore side then you probably have an irritated suture wound which is easily rectified by removing then sutures and rinsing the socket out to remove any trapped food and gunk. I would go see your dentist and ask them to remove the suture as they have done their job after around 7 days anyway.