I'm not an ortho but have similar clicking (only I'm just embarking on my braces journey and hope that a better bite will help fix things a bit). The following advice is what I got from my ortho:
Sounds like it is a little problem in the TMJ (temporo mandibular joint or however you spell it). Most probably the muscles have become tense and tired from opening your jaws for so long and there is a little disc in that joint that can become a little dislocated but it may just settle down on its own once the muscles relax.
It may also be an indicator that you have been grinding your teeth or tensing these muscles during sleep, which could require you to wear a bite splint at night to keep these muscles relaxed and stop grinding on your teeth (its similar to a retainer). My ortho said its a little like you tensing your hand into a claw all night while you sleep and you wake up in the morning unable to straighten your fingers out again properly.
My ortho also suggested I see a physio for relaxation and muscle strengthening exercises that will help. It can also help to reduce stress and have your neck muscles looked at for any tightness.
Hope this helps? And I hope it settles soon