I contacted my insurance first, and they said that under my policy my car was not cover as it was someone who hit me, and not me hitting them. They told me to contact the other party's insurance company, and I did.
Wait a minute. Who told you that?
You either have collision coverage or you don't have collision coverage. If you have collision coverage it doesn't matter who hit who your insurance company would be contractually obligated to pay for the repairs to your vehicle.
If you don't have collision coverage your insurance company is out of the picture with regard to your car damage regardless of who hit who.
Read your policy. Do you or don't you have collision coverage?
As to your predicament with the other driver's insurance the Kelley Blue Book puts your car's value at about $1800. That's the low line with no extra features so you'll want to go to KBB's website and do your own valuation based on the exact model and submodel and features.
I think you will be shocked by the repair estimate. I see about $1500 in damage and that's if the door mechanism still works. If I am close, then your car is a total loss based on insurance industry standards. If you want to keep the car you'll end up with a salvage title and your settlement reduced by the salvage value.
There may be a way to get around that so when you get the estimate come back here before you send it to the other insurance company and let's discuss your options. When you get back here give me the results of the KBB evaluation, too.