Is it possible for my braces to cause tmj pain?

Unlikely: If braces do cause TMJ discomfort, it should very fleeting, and due to a very small set of problems, but in the majority no.

Yes: Orthodontics can be either a part of the cause if they compromise the joint position or part of the cure if they correct the compromises and help maintain stable relationships. You have to first find the stable relationships before you know where to treat. The orthodontics should maintain the stable relationships and not treat to whatever position happens to occur.

Yes: Yes. Ask your orthodontist. You may want a second opinion. Make sure your orthodontist is board certified.