I used to have that reaction when I gave blood until a friend that works drawing the blood told me how to counter the effects.
You need to increase the iron in your body and the best way she said was to eat a steak. If you will eat the steak the day before, should help you counter the dizziness and light headedness.
When you go to give a pint of blood, they always check your iron level before you are allowed to give for those exact reasons.