Illinois is a comparative negligence state, which means drivers can share responsibility for causing a crash. Claiming damages from the other driver's insurance policy can be a challenge when multiple cars ae involved. Each person describes the crash from a different perspective, and the stories may not line up. Do you have collision coverage on your own insurance policy? If so, you may be able to reach a resolution more quickly.
Making a claim with your own company is called a 'first-party' claim. Your policy must have collision insurance on the vehicle, and damages must be above the deductible. Review your policy's loss settlement provisions. The insurance company will pay for damages according to the terms outlined in the policy. Numerous state regulations apply to first-party claims.
Requesting damages through someone else's insurance policy is called a 'third-party' claim. The loss is settled according to the policy terms between the other person and their company. As a third-party you are not part of the insurance contract, and have no rights under it. There are fewer regulations the insurance company must follow on third party claims.