You can go through your insurance company if you have coverage to handle your vehicle. It is a good idea to have your insurance company involved to protect you. After your company settles the claim they will work with the other insurance company to receive the money IF the other party is at fault.
If they are unable to receive the money from the other insurance company it can affect your insurance rates. Typically, you will not see an increase in rates unless you are at fault.
Read this news story about your topic: At Times an Insurance Claim Isn't Worth the Trouble.
Don't forget to get car insurance quotes from CarInsurance.com.