How can I stop tensing my neck (causing veins to show) when I sing ?

Feel the support from your stomach and , fill your lungs, and relax your neck and throat. I find that during practice, it helps to actually place my hands on my neck to feel when it's tensing (or sing in front of a mirror so you can see it happening). When you sense yourself doing something wrong, stop, go back, and do it right. Correcting your mistakes is what practice is all about.