PhatGirl68,
Since it is only on the left side, it is probably not a systemic peripheral neuropathy (like diabetes or thyroid problems).
You may have something going on in the cervical region of the spine. Your description of the pain going into the small and ring fingers goes along with a C8 radiculopathy. However, without an evaluation it is not possible to be exact. As, these symptoms could also be caused by a lower brachial plexus problem or, most distally, an ulnar nerve disorder.
Usually, a cervical nerve root or peripheral nerve problem will not affect the lower extremities. However, a cervical lesion, which presses on the spinal cord, could affect the lower extremities also.
The other option, is that you have two things going on. A problem affecting the upper extremity and another affecting the lower extremity. Depending upon exactly where in the leg the burning pain is located, you could have a lumbar nerve root compression. Or a sciatic nerve problem.
You are just going to have to wait and see what the neurological evaluation picks up. Until you have a diagnosis, it is hard to form an adequate treatment plan. But hang in there.
Good luck.