Car Insurance hasnt called me back ?

Whenever you are involved in a car accident, your fault or not, you need to have your insurance provider to perform all the work. That is what you pay them to do. You should not have any direct contact with either the other motorist or their insurance provider. That is the job of your insurer, make them do their job.

Why are you contacting THEIR insurance company?

Contact YOUR insurer and provide THEM with all the information - it's why you're paying your premiums.

Unless of course you don't have any insurance, in which case you're going to prison and deserve everything you get.

My guess is that they have not completed their investigation of the facts of the loss, in other words to verify if the other driver is at fault or not.

Until they do this will they pay you for your damages, which is the cost to repair your vehicle with a body shop writing an estimate.

The fact that the other driver said they are willing to repair it, means nothing (if) their insurance agrees if liable or not. If they find the other driver not liable, they pay nothing.

Give it till next week and follow up.

You need to inform YOUR insurance company,and give the the info on the other person's insurance company. They're supposed to handle it.