The facial nerve courses through the parotid gland, so it is not unusual for it to be stretched during removal of the gland. If the nerve was not severed and only stretched, normally you should get full return of blinking and smiling, but it can take several weeks to months to come back fully.
Usually temoporary injury will improve over several weeks to a few months if the nerve was not significantly damaged with the parotid surgery. Keep your eye moist with drops or ointment if it is affected. Donald R. Nunn MD Atlanta Plastic Surgeon.