You have the option of filing a criminal case against the driver and a civil case against the employer of the driver. It can proceed simultaneously. Should there be a criminal conviction with corresponding award for damages and the driver has no property to satisfy the judgment, the employer can be made subsidiarily liable. In case you filed a separate civil case against the employer for damages, you are not allowed to collect either in the civil case or criminal case but not in both instances.

I suggest you file both just to be on the safe side. Whatever expenses you may incur including attorney's fees, you can claim it in both cases anyway.