It depends. If your injuries are significant, the at-fault driver has insufficient coverage, or you were hit by an uninsured or hit-and-run driver, you may be making a claim against your own policy.
Also, if the at-fault driver’s carrier tells you that they can’t determine who is at fault without the police report and you need transportation immediately, consider making a claim with your own insurance carrier.
If you make a claim with your own insurance company, you will have your deductible deducted from your repair costs. You’ll be reimbursed for your deductible once the at-fault driver’s policy repays your insurance company.