I have no idea what this is

The right side of my lower jaw has been aching everytime I yawn or open my mouth wide. The very back tooth on the top right side feels like it has a piece missing and is very sensitive to heat, cold, or anything touching it. It's really painful and only a lot of ibuprofen will take it away. Someone please help?

[Jerome Tsang, DDS]

You may have an abscess developing in the area.  It may be spreading around the upper jaw area and causing the lower jaw to pinch against it when you move your jaw.  You should see a dentist and get it checked out.  A root canal or extraction may be needed.