It sounds like you are having neuropathic pain affecting the left arm from the axilla to the fingers. Seeing how you have had surgery on your neck, that appears to be the most likely culprit of your pain. Based on your history, it is likely that your pain is caused by nerve impingement at the level of your cervical spine (the area of the spinal cord that’s located in your neck).
The location of your pain in relationship to your arm can localize the specific nerves that are impinged. If your arm is numb around the area of your upper shoulder to your outer bicep and down to your thumb, it suggests impingement of the nerves exiting your 5th or 6th cervical vertebrae. Numbness affecting the back of your shoulder to the back of your elbow and down to your index and middle fingers suggests impingement of the nerves exiting your 7th cervical vertebrae. Finally, numbness at the area of your triceps to your ring and pinky finger suggests impingement of the nerves exiting your 8th cervical vertebrae or 1st thoracic vertebrae. The information regarding where your pain is exactly located is important for your doctor to determine which level of your spinal cord is affected.
If the pain is mild and there is no associated weakness in the arm, then pharmacotherapy with neurologic drugs such as gabapentin (Neurontin) have been found to be very effective in controlling neuropathic pain. Muscle relaxants have also been used with varied results.
If the pain is persistently moderate to severe, worsening, or associated with muscle weakness, then a detailed medical evaluation by your primary care physicial, a neurologist, or a spine specialist (orthopedic surgeon, neurosurgeon) with associated imaging such as an MRI of the cervical spine is warranted. These symptoms suggest a serious problem which may result in serious, irreversible nerve damage and surgery might be indicated.