Well, a few comments.
First, "correct" extractions on that number of teeth by a general practice vet can be difficult. So, I am concerned they did not properly extract some of those teeth and may have simply burred off the tops hoping there would be no continued issue. That's my first concern. Second, at 2 years of age, I am not sure I would have even agreed to multiple extractions as the solution.
You really need to get him evaluated sooner than later, because I am concerned about underlying pain and/or oral infection.
At least have the ER vet address the immediate issues.
Next, use the ER vet to get a recommendation to see a veterinary dental specialist. Trust me, you will regret not taking your pet to a dental specialist for a second opinion and to review what has already been done to the mouth.
No, extraction of the remaining teeth may not correct the problem, because I am concerned about the condition of some of the previous extraction sites.
You can even use this link to help locate a dental specialist near you: