Hello! Numbness in the left arm and shoulder which is constant in nature is suggestive of nerve compression. Among the causes are a herniated cervical disc and compression of nerves as they leave the chest to enter into the arm (Thoracic outlet syndrome). An MRI of the cervical spine should be of help. Additional investigations like Blood glucose estimation etc and Nerve Conduction Velocity test are also of value in determining underlying disorders and in identifying the exact nerves involved (which in turn helps localise the site of pressure). Do talk to your doctor armed with this information. All the best!