Sounds like tMP is full of folk who clench their jaw at night!
I'm as guilty of this as anyone else (and when I'm not doing that I'm chewing the inside of my mouth!) and believe it or not it does move your teeth slightly.
Now for the science bit...
All your teeth are held in place by a ligament which acts as like a hammock for the tooth and sends messages to the brain saying where the tooth is in the mouth (as you would).
When you grind your teeth or clench your jaw you put pressure on the ligaments which inflame a bit, giving the tooth space to move, hence why it feels weird in the morning.
The ideal thing is obviously not to clench your jaw but as it's a reflex you can't do much about it. Most dentists will, if you ask nicely, make you a gumshield to put over your bottom teeth at night and this just takes the pressure off a bit. Don't do what I do though - more often than not it ends up on the pillow next to me, which can cause some embarrassment

.
Manually realigning your teeth is never the best of ideas - I don't think even orthodontists do that (although one of my patients tried it!). Just try and keep your jaw muscles as relaxed as possible and all will settle down. Mind you if like me you have exams coming up just go into hiding with your gumshield....
Yours grindingly,
Rach x