You can file a claim under your own insurance coverage (and your insurance might turn around and seek reimbursement from the insurance carrier of the person at-fault), or you can file a third-party claim directly with the insurance company of the at-fault party.
If your injuries are extensive, it’s likely one policy’s coverage may not be enough, and you may need to “stack” available policies to get enough compensation for your medical bills, time out of work, and other damages. An attorney can help you do this.