Do we need deep cleaning for 4mm pocket?

Hi, Do we need to do deep cleaning for a tooth which has pocket of 4mm? Can we do deep cleaning on a tooth which was root canal treated recently? have constant jaw pain under ear and neck for 1.5 years now. Have seen TMJ specialist, OMFS, ENT, physical therapist etc. No relief and definite answer yet. Dentist spotted a tooth issue which hurts for tapping and biting pressure on it during my jaw pain visit. Tooth#30. Sent me to Endo. I had root canal on it an year ago. No relief. Same tapping and biting pressure pain on it. Had taken cbct scans. I went to another Endo and he told me that one of the root in that tooth is not filled properly till the end and that could be the reason for the pain.had retreat Rct with medicine last week. No relief. It still hurts for pressing, brushing, tapping. No changes. Is this normal? He said I have Pocket of 4mm in the tooth next to it. #31. Do we need deep cleaning for this? Or goes away on own? This pocket is reason for tooth pain?