It’s certainly within your right to choose your own body shop to repair your car following an accident. I would recommend that you don’t, and the biggest reason is that you want to use a body shop that’s approved by the car insurance company because if something goes wrong with the repairs, the insurance company and that body shop will work it out and they’ll get the car fixed properly.
While using your own body shop, they may charge more than insurance will reimburse, so it doesn’t get paid completely. If there’s a problem getting it fixed, the insurance company kind of washes their hands of it many times, and says, well that’s between you and the body shop, because you’re the one who chose the body shop. So, definitely you should use an approved body shop.