Yes and no. It can depend on whether you have also suffered a physical injury. In New Jersey, the only allows you to sue someone for negligently causing emotional (or mental) distress alone—that is, without an accompanying physical injury—in a few special circumstances. As a general matter, however, you need not have suffered a physical injury to sue someone for intentional infliction of emotional distress.
When a victim has suffered a physical injury, then generally speaking, the victim can always seek damages to compensate for the emotional suffering that accompanied that injury, and for the cost of medical care and treatment of that emotional suffering.