I'm having needle like pain in my chest left side plus pain in left wrist hand and lower arm area plus needle pain shooting to the top of my head?

Needs evaluation. This can certainly be caused from a pinched nerve however given the symptoms of left sided arm and chest pain i would recommend a cardiac evaluation to make sure there isn't anything more serious or life threatening occurring. If cardiac issues are ruled out then an evaluation by a hand surgeon or neurologist would be a good start.
Radiculopathy. From neurological point of view, you may have c7-t1 radiculpathy sxs -means pinched nerve in neck. Other d/d could carpoal tunnel syndrome(pinched nerve in hand). Cardiology point if view, you should see cardiologist to rule out heart attack.