That's just an inflammed piece of gums in the back of your tooth along some food debris . The food lodgement must have caused an infection over there at the back of the gums causing u pain .the tooth nerve might be affected seeing that broken tooth . So the best course of action would be take an xray and pull out that tooth . RCT and dental crown would have really bad prognosis so the best treatment would be to take out that tooth .
Next Steps
get to a dentist let him evaluate take an xray and take that broken tooth away
meanwhile try cleaning the area of food debris and salt water rinse would help to easy the difficulty
Health Tips
don't wait too much so that the tooth gets rotten and all damaged ..earlier the better get it out soon