Hi,
Yes, braces can affect your joint and muscles very, very much so. TMJ is basically caused by an imbalance with the jaw and bite. If your bite is changing while wearing the braces, it will affect the balance. You should be okay if it is just clicking right now. Just be careful about not opening your mouth too wide for too long and you could even consider eating softer foods at this time. Be sure to mention the clicking to your orthodontist. Before the braces are removed, I highly recommend that your bite be balanced, not perfectly straight. There is a difference.
Take care and let us know how you are doing.
God bless...
Carol