Ah,, I suggest you visit our thoracic outlet syndrome forum (aka TOS) you may not have full fledged TOS now but learning about it and the therapies to resolve it are best done before it progresses..

It can become a complex chronic RSI problem if not treated and resolved early.

http://neurotalk.psychcentral.com/forum24.html be sure to explore the Useful sticky threads for a crash course on it.

Having the neck tightness plus the carpal tunnel could be what is called a double crush syndrome. Or the carpal tunnel was a mis dx... very common with MDs that don't know much about TOS...

If you can get some expert PT or perhaps expert chiropractic, for the neck/tightness & posture you may find the hand issues fading..

Your docs might be focusing on the wrong area of treatment..
Hand & arm pain can originate higher up from neck/shoulder/collarbone areas.

Can be trickier if the c spine has some issues but often if your treat the soft tissue & posture things may moderate.