First and foremost, the advice I give is 100% free. Next, you did not have to report the accident to the police but it is always a good idea. A police report can help in determining who is responsible for the accident. Other things to keep in mind after an accident, is to exchange insurance information, take photos of the accident, take notes of what happened while it's still on fresh in your mind, lastly notify your insurance company of the accident. You should report the accident to your insurance company just in case any issues do arise from the claim with the other company. They can be your advocate in getting the claim resolved plus, it is typically required to report all accidents to your company. You can refer to this article
for more help on what to do after an accident. Lastly, the person that hit you is having his insurance company handle the claim which is the best way to handle the accident. If you do not hear from the adjuster in a timely manner then you would want to follow up with his insurance company. Here
are is more information that can help you when filing a claim. Good luck.