Can a pinched nerve in neck area be causing chin tingling?

Not likely. The nerves coming from the spine in the neck do not supply sensation to the face/chin. The trigeminal nerve, one of the nerves originating at the base of the skull supplies sensation to the face. People can have irritation to this nerve, but it's not caused by problems with a herniated disc in the neck.
Pinched nerve. A pinched nerve is also called radiculitis and causes radiating nerve root pain. People typically feel shooting or stabbing pain (can be constant or episodic) and follows a nerve root pattern. Pain can shoot to the chin, or face. It can be caused by a variety of factors and it's important to rule-out red flags like weakness, bowel/bladder incontinence. See your doc, it could be a # of things.