Is the money expected to be received from an insurance company as a result of exaggerating physical injuries considered compensation for psychological damage, and is this money permissible or forbidden?

As for financial compensation that covers actual material loss, there is no problem with it. As for compensation for physical harm, it requires diyah (blood money) if the injury is to an organ, or arsh (compensation) for wounds. Exaggerated estimation of injuries is forbidden and constitutes consuming people's wealth unjustly. It is not permissible to consider this as compensation for psychological damage.