I had braces and retainer for 8 years from age 14 to 22. I wore headgear and later rubber bands. I think they made my upper jaw too small. It is at my far range of motion to close my teeth together and my jaw pops when I open it far. The only time I close my teeth completely together is when I am chewing. We can’t afford TMJ treatment, since the insurance doesn’t cover it.

I feel your pain. I got TMJ after braces too. But mine doesn’t seem to be as bad as yours. Just popping and pain and locking of my Jaw. I sort of learned to deal with it cuz the treatments are too expensive.
It happens, depending on how you were treated. If teeth or jaw were pushed back, yes.
Teach yourself that when you yawn, you touch the roof of your mouth with your tongue – keeps the strain off your ligaments.
I got TMJ after six years of teen braces with loads of elastics connecting upper/lower teeth in various directions. I got major relief after a new dentist (about 12 years later) fitted me for a custom plastic night “splint” because she realized I clench and grind my teeth. It looks like an Invisalign aligner but goes completely over the lower teeth. Within a week the daily pain and popping was gone, and only came back if I was really stressed (jaw clenching). More recently (at age 52) I had braces again to correct a gap that opened up. That process (possiblyby a more competent orthodontist?) has eliminated the TMJ! So, I suggest looking into a splint for night-wear for now (probably under $200, from your dentist), and maybe years from now, more ortho (mine only took one year, and I could finally afford it). Best wishes.