There are several problems that could be causing your left hand pain during sleep. You could have carpal tunnel syndrome, a pinched nerve in your arm, or a disk problem in your neck. Each of these problems can cause pain when the area is laid upon while sleeping. Mention the pain and ask for an MRI next doctor visit.
The pain in your hand could be circulatory. Also, a systom of Carpel Tunnel Syndrome is a "tingling" sensation felt at night. A pinched nerve could explain the pain.
It could be because your heart is not receiving enough blood for some reason. If you are sleeping on your hand, it might also just be nerve compression.
This could be the beginning of carpel tunnel syndrome. Once you are asleep, your hand will fall into a natural position that may be pinching the nerve that runs through the tunnel in your wrist. An orthopedic surgeon will order a simple electronic test that will determine if the tunnel has been constricted and offer options.
This pain in the arm while sleeping is most probably caused by the way you are sleeping. When sleeping sometimes nerves are compressed usually in the shoulder area.
You might have practised sleeping by keeping your left hand under the head. People having heart ailment also may have pain particularly on left hand. Better to consult a Cardiologist and confirm that your lipid profile test is normal. Avoid sleeping by keping your hand under the head.