I heard that tmj can cause sinus problems, so there's an increase in bacteria hence the bags under your eyes. You get bags under your eyes because of build up of bacteria in the lymph vessels.
A physiotherapist can do Manual Lymph Drainage on your face, it takes a long time before they might disappear, and it's a hard treatment for the therapist him/herself because of the low&constant pressure.
But hey! They are the ones getting paid right?