I just wanted to reply to let you know I am going through something very similar. I had recurring tonsil infections, got my tonsils removed, and tonsil tissue still remains two years after surgery.
Since my surgery I have had recurring left tonsil infections that would go away with a course of antibiotics. But about three months ago I had what seemed to be the same infection but has not gone away with antibiotics this time. Like you, I am experiencing severe pain through my jaw and neck and also frustration over what it could be - all my tests have come back normal (not mono, blood count is fine) and also no fever; but my tonsil is visibly inflamed and full of puss. I have been waiting on surgery to have it removed again for three months, still two more weeks to go.
Will follow your post and hope you hear back some possible causes soon.
Wishing you good health,