Unfortunately, you probably cannot. The law does not, as a general rule, compensate people for being scared, upset, traumatized, etc. by close calls. The main situation where someone can get monetary damages for purely emotional or mental injury is the tort of "intentional infliction of emotional harm"--which as the very name of the tort indicates, requires an intentional or deliberate bad act, not merely negligence, such as is typically the case in a car accident. You can certainly contact a lawyer to discuss the case and see if he or she believes that you can recover, but bear in mind that it is usually not the case that you can recover for a "traumatic experience" when there is no physical injury and no intentional bad act.