I wouldn't worry that there is something wrong with you because you feel faint with having blood tests done! A very large percentage of the population has this problem!
Essentially what happens is that in some people, in response to the sight of blood or another stressful stimulus, the body can trigger a neurological reflex that causes blood to pool in the legs and the heart to slow. This results in dizziness
and can even lead to fainting as the blood flow to the brain diminishes momentarily.
In order to minimize this problem you can continue to do some of the things that you are already doing - such as making sure that you are well rested and have eaten a meal when you go to get your blood drawn. You can also ask your doctor
to clump tests together so that they can happen infrequently as possible. Finally, and most importantly, you should always let the person who is drawing your blood know that you tend to feel faint when you have procedures done. They will make sure that you are seated comfortably or lying down so that there is not chance that you could fall over or otherwise injure yourself.
Ask your primary care doctor
for more information about this issue!