If you have any of those bulky box fans, get them out and start them up. You want to do what you can to dry out all the damp areas within 48 hours to prevent any mold from forming. If you notice something growing, use a diluted bleach solution to wipe the area.
The parts of the ceiling that got wet, may start to crack/peel about 5-7 days from now when it's completely dry. Don't bother fixing it till spring/summer. You want clear all your furniture underneath the damaged area before they repair the drywall, sand, prime & repaint.
I'll be doing the same thing this summer.
I think I had at least 100 gallons go through my 3 ceilings before I could figure out which water valve needed to be shut off.
Thanks for posting the pictures. Brings back some horrible memories that I hope I don't have to witness again.