I would agree with going back to the dentist who took out your tooth. They have medicated gauze that can help sooth and heal the bone and you need weekly follow up visits until the problem is resolved. 3 weeks is much too long to have dry socket if its getting taken care of properly.
Going back to your oral surgeon to have a follow-up exam is advised.
I just had a wisdom tooth pulled. I was experiencing simular symptoms. Only about a week long though. Anyway, I went back to dentist, it ended up being food that had gotten stuck in there causing the pain and inflamation. What's your dentist think??