actually the pain in the left hand and the numbness appears because of the pressure on the nervious which comes to the upper limb(left upper limb).
It's usually it is because of disk prolaps.(Cervical Disc prolaps).so there are many discs in the cervical spine so this discs are nothing but soft tissues in between the balls like this image,
so for every vertebra(that is what we call the heart of the backbone) that will be an adjacent disk. so these discs a soft gelatinous catilage structure which are there too just to cushion the spine. so it is given flexiblity to the spine.
when this disc weakens it sometimes stress , because of the stress and strain .when its tears it comes out from there and process upon that narrows.so when the disc tears and presses upon the Narrows so the narrow starts painting. so wherever the narrow runs it use when pain. usually depends upon the level of the disk in North. suppose it was an upper cervical disc then the pain will appear in the upper part of the neck and in the back of the head.if it is a lower cervical disc the pain happiest in the neck upper part of scapular region then shoulders forearms and hands and sometimes people may experience numbness also. sometimes people confuse it with the cardiac pain.because the left side pain usually ,they are confused for heart problem.so but usually hard problem if it's only in the shoulder engine and in the upper part of the chest.usually it doesn't run below the elbow.so if the pain is there below the elbow, and the hand certainly it is not because of the heart problem.It is usually because of that disk collapse(cervical disc prolapse) though you get pain and numbness in the upper limb.