chest pain along with a left
arm pain and stinging sensation in the fingers sounds to me like a cervical nerve being trapped.
Most commonly seen in cervical spondylysis or if a
cervical rib is present which is putting pressure over the nerve.
Get an xray of the
cervical spine and see an orthopedician for further help.
Another possibility can be a SLE which will cause such pain however left arm pain is something unusual.