Wow, you're really kind of all over the place here. That's two questions plus a half-question, all from one minor accident. But since you asked...
Yes you were rear ended. (That was your first question) Thank you for asking and glad I could help, I guess. And yes, yes the other insurance company will look into this. They'll look at the repair estimate and compare that value with the appraised value of your vehicle, and if the repair cost exceeds __% of the vehicle's pre-accident value they'll declare it a total loss. I left the percentage number blank because the magic percent varies by jurisdiction, and you forgot to mention where you live.
Where you go from here is exactly where you have already gone. You've reported this whole thing to insurance, so let them do their thing and they'll let you know as soon as they can. You've got an older (not ancient, but older) vehicle with mileage on it, so don't expect a huge settlement. Insurance companies only cover the Actual Cash Value (depreciated retail value) of a vehicle, nothing more.
I'm not an appraiser and neither is anyone else in here, but I seriously doubt your vehicle is worth ten thousand or more. That means if your vehicle is a total loss, you'll still owe money to your lender after the settlement is paid. If you purchased GAP coverage, now is the time to use it.