Hey I recently injured the right side of my neck and everytime I turn my head to left I can feel a vein pulling from head to shoulder should I worry?

There's no vein. You've likely pulled a muscle of some sort. If i were you, I'd consider getting the neck examined and then, getting physical therapy or whatever else the doctor might suggest done and you'll start to help better.
That's not a vein u. feel.Its likely some muscle soreness/tightnessWhen u turn your head to the left,you relax and stretch the R neck muscles.Try gentle stretching regularly.If gets worse or doesn't improve,c ur doc.