If you feel pain and numbness from your left shoulder to your arm, the first thing to consider is frozen shoulder, as frozen shoulder can cause pain and numbness in the shoulder area. When frozen shoulder is more serious, the pain and numbness can be radiated to the upper arm area, so you should seek medical attention to determine the cause of the problem so as to avoid delays.
There may also be a cause of cervical spondylosis, and a cervical spine X-ray or magnetic resonance imaging (MRI) can assist in the differential diagnosis.