Hand washing vs hand sanitizer? Which is better when done performing blood draws! Would hand sanitizer prevent me from getting infected?

Both work. It's my understanding that hand washing and hand sanitizer are both good; certainly they are far better than not washing hands. If you are drawing blood, wear gloves. Don't re-cap needles, because you really can get stuck. If you should have a needle stick injury where you are in contact with a patient's blood, call your supervisor, the nursing supervisor, or the employee health department.