Sorry to hear about your accident, and sorry to hear that the insurance company is playing games. Sadly, you should be prepared for a few more of their tricks.
The insurance company is in business to make money not pay out claims. They're going to do all that they can to avoid paying for your damage. On top of it all, the guy who hit you may have told them a bogus story about what happened. The insurance adjuster is allowed to believe that lie even if it's obvious.
You don't have to use their repair shop. You can take your car to any body shop you want. The other guy's insurance company will tell you that if you take it to their "preferred" body shop, they will pay immediately. It's a scam to send you to a place that uses cheap Chinese replacement parts and cuts corners on repairs to save the insurance company money.
There are things you should do first: 1) Get an accident report from the local police department; 2) Go the hospital if you are in any discomfort as a result of the collision; 3) Don't make any statements to the other guy's insurance company about what happened and how you're feeling; and, 4) Talk in person with an experienced Personal Injury attorney. You need to protect yourself and your wallet.
Any of us will give you a free consultation to discuss your rights, and what should happen next. Good Luck!
If you have auto insurance then contact them and start the process of getting your car fixed.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.