--to get a workup at a tertiary center that specializes in neuromuscular diseases.

As regards that lumbar disc problem, it certainly could explain sciatic symptoms, but not what's going on in the rest of your body. (And yes, it is possible for bulging or even herniated disc material to heal and be reabsorbed in time, resulting in reduction of compression on nerves.) But if you are having symptoms above the level of the lower back/leg you need to have a more thorough investigation done, and yes, they need to MRI your bran and spinal cord to look for diseases of the central nervous system, such as MS, as well as test you for conditions of the peripheral nervous system (that which is outside the brain and spinal cord).

There are many autoimmune conditions, such as lupus, that can secondarily lead to neurological symptoms, either through direct autoimmune attack on nerves or nerve compression.

And sensorimotor is just a way of describing what modalities are affected--when they put "sensori" in front of "motor" it's a way of designating that both sensory and motor symptoms are involved, but that the former are greater than the latter. (One could also have autonomic involvement.)