Numbing shots for diagnosis of my pain.

I have been dealing with lower jaw pain under ear and side of neck for more than 10 months. No injuries prior. It's like burning and sore pain in the jaw under ear and neck. Been to multiple doctors and dentists. They said it's Myofascial pain dysfunction. I do have muscle tightness and stiffness.  I have 2 lump like spots in jaw under ear and neck. The lump in neck is pea like size and hard. It's the same from June'20 till now. No change in size. My physician ordered neck ultrasound and CT scan to check. Extracted upper wisdom tooth and rct on lower molar 46( suspecting tooth root fracture,cbct clear,no cavity. 46 hurts for tapping and biting pressure before and after RCT )Pain is constant under ear & neck. My dentist told me to check about Eagles Syndrome. He said it's a rare condition and wanted me to check with ent/OMFS. 46 hurts for tapping,biting pressure. dentist want to try numbing shots to see if cause of my pain is from that tooth or not. is it safe? how to find find fracture