Severe pain in left shoulder/arm and down left side?

See doctor. Its important to establish a diagnosis. Shoulder/arm/radiating pain could be from 1) referred sources including: neck, abdomen, and heart. 2) shoulder sources include: arthritis, labral tears, instability, tendinitis, rotator cuff tears, bursitis, painful bony spurs etc. Therefore proper diagnosis is essential to stopping the pain. See an orthopedic surgeon.
Varable. Does it hurt with shoulder movement? It may be joint, shoulder , muscle in cause. If not, concerns are heart, lung and either way you need a full history and appropriate exams.