A lower disk herniation, or budge, "shouldn't" cause neck issues as well, however, it still can. When a disk herniation causes discomfort, it tightens the muscles around the area in the body's attempt to prevent further injury and reduce swelling. Same as if you sprained an ankle or cut a finger.

When the muscles in the lower back tighten however, it changes ones posture which often times places strain on the neck. When I herniated and bulged an L3 disk (and broke the vertebrae) it wasn't long before I pinched a nerve in my neck, though I followed the doctors directions, was doing PT, taking meds, and not lifting more than 10 lbs.

I still have a lot of problems with my neck and left arm, exasperated by MS and a bad car wreck (now I have a bulging disk in my neck ) but the MRIs showed that the vertebrae were already showing undo signs of wear and tear in the ten+ years my back has been injured.

I've never gone to a chiropractor, went through orthopedics with my back, who referred me to physical therapists rather than a chiro. My brother had a similar injury, around the same time oddly enough, and went to see a chiropractor for his back finding less improvement than I have (even with my compounding issues). But then his injury was the result of downward forces (fell from the top deck of a naval ship to the lower managing to land on his feet) while mine was spontaneous combustion for lack of a better term.

What you're describing is extremely similar to what my brother has complained of in terms of symptoms. Which still doesn't rule out MS, it's entirely possible to have both, but the symptoms you describe are more classic back injury symptoms rather than MS.