My DW was a victim of hit and run last year. They caught the guy not long after. Her POV was taken to a shop and within a day or two was marked as totaled. Neither insurance covered a rental at that point. We have great ins. He had Safe Auto (not great).
We end up borrowing an extra car from our extended family. It was a junker that I eventually put about $700 back into it before returning it. So yeah, we lost money on that but when the POV was paid out the former car payment became maintenance payment. But it solved our problem for a few months.
We nowhere came close to recouping our financial, emotional and physical losses in that accident. I hope that things work out well for you.
Word of advice. Do not baby or alibi any potential injury. If you suspect whiplash schedule an appointment now. Then when they give you physical therapy do not miss a single session. They give you 10 sessions. Complete 10 sessions. or whatever. If they diagnose a problem and you decide you're too busy to make the appts or start feeling better sooner so you stop going, you are going to kick yourself when you try to settle this for the most amount of money you can.
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Don't just survive. Thrive.