Your spine send out nerve roots that follow dermatomes - these are innervated areas that extend all the way around your front, side and back in bands.
A pinched nerve
from disk disease can cause both back and chest pain
and we do see it from time to time. See this diagram: https://www.Google.Com/search?Q=dermatomes+of+the+back;newwindow=1;rlz=1c1chwa_enus535us535;espv=210;es_sm=122;tbm=isch;source.