There is no reason why your insurance should go up--you were just sitting there minding your own business. Nor should you have to pay your deductible.
Do NOT talk to your insurance company by phone beyond reporting that there was a collision; get the police report, and answer written questions in writing. They will try to trap you into saying something was your fault when it wasn't.
I'm glad you are ok. The car is only a thing.
After I got rear ended, my rearview mirror became my new best friend. Still is, and that was back in 1989! I make sure it looks like they are stopping, and if they are moving too fast to suit me, I hit my emergency flashers to get their attention off the *&^#()%$ phone! I also never get right up against the car in front of me so that I can try to get out of the way of someone about to hit me, perhaps. At least, I have less chance of hitting car in front of me. And my foot is on the brake, hard.
I drive as if everyone else on the road is stoned, drunk and out to get me. I have zero trust in other drivers. And things have gone well ever since.
Sharon
So far, so good.