When I turn my head I hear a faint swishing sound at my neck. Is this normal?

Not necessarily. Sometimes blockages within the arteries of the neck can cause "swishing" sounds. The medical term for this is a "bruit". In the neck this is most often from the carotid artery. The sound is created by turbulence in the blood vessel created when the blood is flowing past a blockage / narrowing. A very simple and non-invasive test for narrowing in the carotid arteries is a carotid ultrasound.