Orthognathic surgery will change your bite, but most likely not change your pain. Your teeth and how they 'match up' are seldom the cause of pain. Your pain is most likely from adverse loading of the TMJoint or disc displacement in the TMJ. Either way the source of the pain needs to be diagnosed and treated before any orthodontics or surgery. The research literature backs me up on this one. Find a good TMJ specialist that works closely with an orthodontist or is an orthodontist (there aren't many of us unfortunately). Physical therapy is only part of a good team, not the answer by itself. I use PT's with 90% of my patients to help shorten treatment times. Hope you find some help. TMJDoc
See your doctor and ask if you can have physical therapy, they have those that specialize with TMJ
i tried a splint called the "aqualizer".. it helped, temporarily (see link below).. i see you have tried muscle relaxers.. was magnesium one of them?
also, assuming that you have seen an ENT.. is your ear health in check? what about possible teeth needing filling.. etc.. sometimes dental problems and ear problems can manifest themselves in the jaw.. it is all related.. as i am sure you are well aware..
do you suffer from allergies? i notice that any time my sinuses are inflamed, my jaw feels sore.. the pressure is felt in the entire region.
http://www.aqualizer.com/index.html
Seeing an orthodontist and tmj specialist is advised.