Can I go after the at fault insurance company?

The key issue here is the fair market value of your car. If the repairs to your car would cost in excess of the value of your car, then the insurance company can "total" the car and pay the market value.  Insurance companies tend to be pretty consistent with property damage, so you may get a similar response from the other company. You can take a run at the other driver's insurance.  However, your options are somewhat limited as the other carrier may likely respond as your own insurer did.  Note too that if your car is totalled, then you do not get a rental car.