When I started cpap 11 months ago, I quickly experienced very stiff jaw muscles. I was using a Swift nasal pillows mask. I have a small face and am a side sleeper. I also sleep very lightly and the whole cpap experience was a nightmare for me.
I think I was very anxious about the cpap and exhausted, and that I was holding my head and neck at a weird angle to keep from dislodging the Swift. After a few months I switched to a ComfortLite 2 nasal pillow mask that works better for me as a side sleeper.
Apparently I do not have TMJ. Apparently my now chronic jaw muscle stiffness is stress related. I feel like I have tried everything and been to every medical practitioner (physician, dentist, sleep doctor, chiropractor, ENT, and now physical therapist).
The doctors wanted to go the pharmaceutical route and treat me for anxiety/stress. Several meds they tried me on had really bad side effects that I could not tolerate.
I am better now, but not back to normal. I have gotten some relief from a low dose of anxiety med, the physical therapy and the jaw exercises I do on my own.
The cpap therapy is so important and I have somehow managed to be mostly compliant through these jaw issues. My advice to you is to go to a dentist who has some understanding of sleep apnea. Also, do consider physical therapy (find one who specializes in TMJ).
Finding the right mask is also key. If you are a mouth breather, you have fewer choices unless a chin strap or mouth taping works for you. Do a search on this forum about TJM, jaw pain, ear pain, and throat pain. You will see it is not an uncommon experience and you may find some helpful tips.
I wish you the best.