I have also had TMJ as far back as I can remember. Thankfully it's better today. It's just not as bothersome now as it has been at times in the past. TMJ can be very painful and it can bring about all kinds of problems for us like headaches, ear aches, sleep problems, eating problems, etc. My mouth still makes that clicking sound sometimes when I chew. It totally annoys the members of my family who have heard it for so many years.

Some foods make it a lot more noisier than others and that even hurts sometimes.
I know that mouth guards are commonly used for treatment to help keep the back teeth from clenching and grinding so badly. They often refer to the mouth guard as a splint. These splints or guards can cause dental problems with our bite however so even they are not really good for a lifetime of use.
As far as medications go both muscle relaxers and benzos are used. The muscles of the jaw, face and neck all tighten up and what not during an attack if you want to call it that.
Soma could help some with most of these problems. And nothing makes us clench and grind our teeth worse than stress.

So both types of meds are used. But these types of meds are to be used short term only, not continually for a long time. TMJ is a tough problem to treat medicinally on a long term basis.
There are actually joints in both sides of our face just in front of the ears. I forget the exact name of the joints but this is where the name TMJ comes from. Since these joints become inflammed during the process of grinding, clenching, all of the things we do that cause TMJ pain, NSAID medications work about as well anything in trying to treat this with some sort of a maintenance drug.
Motrin or
Ibuprofen 800mg are good medications for this problem on a longterm basis.
People who have never experienced TMJ have no idea how annoying and really painful it can become. For me it has always been one of those things that isn't all that noticeable and then suddenly it flairs up and really hurts.
I would recommend that you try taking either Ibuprofen or Motrin 800mg three times a day as needed when the TMJ bothers you and continue to take the soma as well, just in a lower dose. You didn't mention how much soma you were taking a day or at a time. Soma can be rather intoxicating if we take too much. It would be nice if you had a low dose benzo available in case you needed it but doesn't sound like your dr will work much with you. These drugs are very addictive and I am sure he is trying to make sure this doesn't turn into a major problem for you. Surely he won't have any problems with an NSAID. Hope this helps a little. I know TMJ is a difficult thing to get an answer for. Good luck.