Mild broad-based posterior disc protrusion at l5-s1 but no nerve root comprression doc says not be causing my pain what else could case my pain?

Mechanics: You can have low back pain due to poor biomechanics - meaning your spine is not well aligned and / or you have unequal strength / flexibility in the muscles. Being out of shape can worsen back pain as can smoking. I would consult a chiropractor and begin an exercise program designed to improve core strength.

Your back is chock: full of layers of muscles, ligaments, joints, etc. Any problem area can lead to radiating pain.

Spine Injury: This pain in the distribution as you suggested is the result of an irritated nerve or facet joints or other injury typically in the lumbar spine (low back). I would seek further evaluation by a spine specialist.