Lower back pain along with right buttock and right hip pain. Painful during movement. Looking down with chin on chest causes shooting pain down back.

Sciatica. Although there are several possibilities, one if the more common causes is a sciatica, which is an irritation of a nerve in the back that can cause pain that runs into the hip. When you lower your chin, it increases the pressure in the spinal canal and can aggravate the symptoms like you are describing. The hip and the SI joint are also potential causes. Don't hesitate to be seen.