As a veteran of a number of conflicts in the region:
-Register with the embassy but remember they are not miracle workers and their local staff are under the same shelter in place guidelines. No one is going to send a helicopter.
-Flights usually start up again quite quickly. I always keep an eye on El Al (the Israeli airline) who are often quick off the mark.
-Bur remember a lot of planes and crew will now be in the wrong place and there is backlog. It might still be some time.
-Statistically, your chances of being hit are very very minimal. But I would still stay away from very obvious western aligned places like very fancy hotels or malls and keep your curtains drawn. Know your exits (this is good practice in any hotel).
-I always have a grab bag when I travel and am the chillest person ever. There's no harm in it and make sure you include spare pants!
-Misinformation is rife. Only check official or reputable news stories.
-Don't try and drive out. Borders are some of the worst places to be. This is especially true if you don't speak Arabic.
Hopefully you can chalk it up to a few annoying days in the not too distant future.