Can severe carpal tunnel syndrom cause other issues? shooting pains in elbow, back of the shoulder and aching in the base of the neck?

Carpal Tunnel: Carpal Tunnel Syndrome is due to median nerve that passes through a narrow canal at the wrist becomes impinged due to swelling. Typically, there's discomfort downstream from your wrist (hand/fingers) and not the elbow, shoulder and neck. You may have a herniated disc at the neck area causing issues downstream i.e. back, shoulder, elbow. Consider further eval w/Healthtap or your primary care MD.