If you back in to someone and they say they will Handle with out the insurance company but need a week or so to get estaments what should I do?

Don't believe them. Call your insurance company and let them handle it. If you don't, you could end up paying for something that you are not even responsible for. And the people could come back through their insurance company later and get you to pay again. The best thing is to call your insurance company, that is what you pay for.