If we done a blood draw from the arm (elbow), and later develop a sort of tinging or jumping sensation of the vein or nerve there and still persists after1 year what could be wrong? is the blood draw procedure damage the nerve?

venepuncture can cause nerve damage. the oft used antecubital fossa at your arm has the median & radial nerves that can get nicked by the needle, but it would generally be described as much more painful than standard needle puncture (and happen after needle entry). and resolve fairly quickly without persistent effects, or at the most a few weeks.

but persistent feeling over 1 year? first i've heard of it.