The driver has constituted the crime of causing traffic accidents and should be subject to criminal punishment. The problem is not whether he should be handed over to the judicial department or the court, but that the transportation department should take the initiative to hand over the driver to the public security organ for investigation and be prosecuted and tried. In other words, the driver must be sentenced by the court for traffic accidents.
As a victim, when the driver is prosecuted in the procuratorate, he can entrust a lawyer to represent him in the prosecution of civil compensation.
Even if there is no criminal offence that constitutes a traffic accident, you, as a victim, can directly file a civil lawsuit with the court and demand compensation from the driver.
This case can't be settled privately, because the traffic police have been involved.