Yes, you can, as long as you suffered a tangible physical injury. If you are filing a wrongful death claim, the deceased victim’s injuries will be sufficient to qualify you to claim damages for emotional trauma (known in legal parlance as “non-economic damages”). “Pain and suffering,” for example, is designed to compensate you for physical suffering, while “mental anguish” is designed to compensate you for the psychological suffering you might experience if, for example, a catastrophic injury left you unable to walk again.
It is extremely common in a lawsuit or a settlement for the amount awarded for non-economic damages to far exceed the combined amount awarded for economic damages such as medical bills and lost work time.