It IS a spinal issue! Whether the Chiropractor says so or not.
I would see a different Chiropractor and/or a spinal specialist to make sure, but from my experience with bones, spines, (my own) and Chiropractors and spinal surgeons, I would say that you have a pinched nerve in your neck.
It is POSSIBLE that the lumbar spine plays a part in this but, your symptoms would indicate the neck being the problem rather than the lumbar spine!
Try another Chiropractor or a spinal surgeon and see if X-Rays or and MRI will give you your answer!
Do it NOW, before it gets worse. It could be that another Chiropractor will be able to manipulate the neck and get all of it to go away, by moving the impinged nerves out of the way through manipulation.
Good luck!
Personally I wouldn't let a Chiropractor touch my neck, although I have had a couple neck surgeries, but even if I hadn't. It's just too dangerous. Go see your PCP and get a referral to a Spine specialist for an evaluation. Then maybe you can see a Physical Therapist or Osteopath that specializes in Neck and Back problems.
I do see a Chiro for my low back and he's helped me tremendously, but neck's are a different ballgame.