Yes, the ulnar nerve actually starts at the side of the neck, where nerves are connected to the spine and exit through small openings between the vertebrae. The ulnar nerve travels through the shoulder, down the arm and around the elbow, terminating in the hand.
I too have shoulder pain that I feel is related to my cubital tunnel syndrome. The pain in my elbow seems to flare up at the same time as my shoulder pain.
Thanks for writing!