If you were at fault in the car accident then you can help to lower you car insurance payments by taking a driving course after the accident and you should also let your auto insurer know about the accident as some insurance companies will work with you and not increase your rates.
The insurance company will eventually find out about the auto accident anyway so telling them is the best thing.
You can also increase your deductible and even ask if your insurance policy has accident forgiveness.
If your insurance rates stay high you can also shop around for a new insurance policy with a lower rate and find an auto insurance company that has accident forgiveness.