There is no way to force someone to use the phone.
The first and most important step is to stop calling. Every time you try to call, it sends the message that if they continue to ignore you, then all you will do is to make more phone calls.
The next step is to send a letter by certified mail, return receipt requested. This is often done just before suing, so it may scare them into thinking that you're about to sue, and that might prod them into action.
If you can't find any other solution, you can sue the driver who was at fault (not her insurance company) and if you win, then her insurance will pay you. However, doing it this way will take a lot longer than just a few weeks,and sometimes even takes a few years.