The reason people get sick and light headed when they're anxious is because of hyperventilation.
Lightheadedness and sickness feeling from anxiety or nervousness is mostly attributable to hyperventilation.
When a person is suffering from anxiety your body triggers a reflex known as the fight or flight response and so you can start hyperventilating and becoming lightheaded and dizzy.
It's normal to get sick and light headed when you're anxious as your body naturally triggers the fight or flight system, which a natural reflex that is designed to prepare your body for rapid action in order to evade threats.
If you start feeling dizzy or light headed and are suffering from anxiety then you should sit down or lay down and try breathing into a paper bag.
Most times you'll feel better after a few minutes or so.