Stan,
Thanks for writing, but I'll need some clarification from you. You said at the beginning of your question that the pain is in your left shoulder and left hand. But then at the end of your question you mention the pain in your "arms" - is the pain just on the left, or on both sides?
Warm wishes,
AT
Stan,
Thanks for clarifying that it is just your left arm.
A full examination would be necessary to tell you the reason for your pain. Finding a local evidence-based chiropractor in your area would be something for you to consider. They will perform the diagnostic tests necessary to answer your question more concretely.
From your brief description, it could be an irritation to the muscles or nerves near your lower cervical spine. Muscle spasm, strain, or nerve root compression in your neck can cause the radiating type of pain you're describing, and be helped by chiropractic care.
Best of luck.
Warm wishes,
AT