Is it permissible to seek financial compensation for a run-over accident after the perpetrator has covered the treatment costs and the injured party's professional life has not ceased?

For injuries that do not have a prescribed blood money (arsh) stipulated by Islamic law, the physician's fees are borne by the aggressor. However, this is not the case for injuries that do have a predetermined blood money. The final arbiter in cases of disputes and contentions is the Sharia courts or their equivalent among the people of knowledge.