What does it mean if i have a headache on left side of my head that spreads down neck, shoulder, and arm?

Nerve and/or muscle: A squeezed nerve exiting the spinal cord in your neck may be the cause of all the pain. If so, there may be associated loss of sensation, tingling, weakness and when severe, shrunken muscles. Another common cause of your symptoms is muscle generated pain. The muscles in your neck and shoulder, especially if they are stiff and tender, may cause pain radiating to your head and down your arm.

Cervicogenic Headach: You could be having cervicogenic headaches. They are typically referred from the neck to the head but I have seen patients having symptoms of head pain which refers to the neck, shoulders and arm. You may require a combination of physical therapy, posture training and short term medications. Pcp might be a good starting point.