What does it mean to have narrowing in the disks in my neck? and could this be also causing extreme pain in my shoulder?

Degeneration: Discs in the neck serve as shock absorbers and space maintainers and help keep the neck mobile to twist and turn to look around. Discs can degenerate and thus narrowing between the vertebrae occur. The nerves coming off the spinal cord exit at the levels of the discs. If there is too much narrowing, the nerves are "pinched" and pain results. Yes, this can be in the shoulder and go down the arm.

Lots of things: It could be anything from arthritis to nothing. Your doctor will be able to at least start you on the right path.