The problem is that you're in "limbo land." I've actually been there myself. What I mean by limbo land is that I have to assume either you haven't filed a claim or the other party hasn't filed a claim yet so in reality the insurance companies aren't fully involved. Nothing gets moving until all insurance companies of involved parties are ... well, fully involved, and that usually takes 24 hours during the business week.
We had our car get totalled while it was PARKED -- legally -- in front of our house on the weekend. Since the person who did the hitting hadn't called their insurance company over the weekend my husband wasn't able to go rent a car to go to work (first marriage, we didn't have a credit card then). Once the other party contacted THEIR insurance company a rental car was delivered to our house that night, but it took 24 hours.
Generally speaking, if you want things to move faster than the insurance companies are capable of moving you end up having to go into your own pocket and saving receipts, which get reimbursed when the claim is settled.