I'm really happy this topic came up.
I too have been diagnosed with tmj. I played a lot of violin, and my posture wasn't the best, and over time, along with my crowded wisdom teeth moving it out of place, I have to fix it with a splint.
I want to say that there are so many factors that can lead to tmj- straining your throat, back of mouth, and tongue when trying to speak in a higher register probably exacerbates your symptoms, but it might not be the core problem. The pain is reversible, though, and as well you should be able to keep speaking at your desired tone.
It could be because it's hard to consciously and consistently relax your muscles, which then produces strain. It could be because there might be a slight misalignment with your bite. How far are you into the diagnosis?