@KWC
TMJ disorders typically start with some type of trauma, such as head and neck whiplash, overstretching of the lower jaw, or trauma around the lower jaw or chin. The resulting injury to the ligaments within the TMJ results in slippage of the disk.
Any of this can cause somatic tinnitus. Whiplash may happen from lifting head off a dental headrest when pressure is being applied to lower jaw. Tinnitus from his is usually caused from muscle spasms in neck that press on C spine, causing nerves and sometimes arteries to become inflame. The jaw should be rested for a few minutes during dental treatment.
https://www.tmjsurgery.com/AboutYou/Overview
The temporomandibular joint (TMJ) acts like a sliding hinge, connecting your jawbone to your skull. This can cause pain in your jaw joint and in the muscles that control jaw movement and when severe, swelling will happen.
Treatment for the sliding hinge is needed later and not by exercises.
Trial and error: Either warm or cold to see what helps.
Done by ringing out a washcloth. Apply for a couple of minutes and if some relief, use for two minutes or longer - 6 times a hour. Continue as needed to bring down the swelling.
I would focus on this for now. You have an jaw injury and I would not mess with other treatments for now, unless you have a toothache.
Besides muscles interaction and nerves, you may have some infection, from injury. Infection from shifting of teeth with having an injury. Clinching of teeth, pressing teeth together or by a splint could cause a shifting of teeth infection.
TMJ steroid injection may be needed with inflammation - swelling and pain. Should be done by an oral maxillofacial surgeon.