Usually it is the way of breathing that changes, because of anxiety (fight or flight state). The pace and volume becomes imbalanced with respect to the oxygen / co2 needed, even when no hyperventilating seems to be happening. This imbalance causes lightheadedness and ultimately dizzyness or passing out. One trick that can help, when you feel like that, breathe in deeply and the breathe out very very slowly through a fine opening between the lips. Then pause several seconds and repeat. This can be done without anyone noticing, because it is subtle and slow.