Third molar root remnants present. Dentist said no problem. But, having pain for more than 3 weeks

[Niko]

My brother got his mandibular right third molar extracted 3 weeks before. His dentist took 4 hours to get it out during which he had to keep his mouth open for the entire time. After the extraction, the dentist said some portion of the root is still present as it is twisted and also calcified at some spots. Due to so much chair time my father asked him to relieve him off the chair. He sutured it and said it's not much problem, it will heal on its own. He was having great pain after he came home which continued everyday.
After 8 days we couldn't contact the dentist to whom he got treated, so we took him to another clinic. He cut the suture and said he got 'muscle sprain' on the right cheek due to such long procedure.
He also got bruses on his right side of the lips and adjacent region due to instrument abrasion.
He tried to increase his very much lowered mouth opening using forceps sort of an instrument. It did increase for some amount but he was having increasing pain during the procedure.
The doctor said he need to move his mouth if he wants to improve his opening. He advised using chewing gum for mouth exercise.
After he came back he still had that sharp pain which is spread from near the ear region to all his right side of the mouth.
He says he gets burning pain on his mouth.
Sometimes the pain is relieved but if he sleeps or after he had food, he just can't bear the pain and have trouble, almost phobia to sleeping.
We talked with the 2nd dentist to whom we went later, he said it's ok it will heal.
But it has been total of 3 weeks but he has no sign of improvement.
I am in a desperate situation please help.
Also, he has sensitivity on his anterior teeth which was not present before extraction

 

[MattKW]

It sounds as if his continuing pain is from the lengthy procedure and rough handling. Broken root tips are common but rarely lead to problems when the tooth was alive at time of extraction.
Please, do not chew gum or have strong opening pressures applied. This has no benefit at all and may only worsen his issues. Instead, try the highlighted suggestions in this article. Maybe go back to the original dentist for further advice.