What nerve runs from back of skull into left eye, down left side of face, into left shoulder, arm and fingers. not pain more numb/tickle sensation?

None does all this: The occipital nerve emanates at the back of the neck, travels up the back of the skull above the ear to the side of the skull. The supraorbital nerve is above the eye. The facial nerve doesn't extend to the shoulder or arm or fingers. Sensation in the arm and hand stems from a nerve root at the neck or from the brain(cortex) itself. A neurologist can advise you best.

There is no one nerve. Your complaints suggest a problem in neck or left brachial plexus. See a neurologist, and consider EMG testing and imaging of neck.