Lightheadedness as you describe is caused by lack of blood flow to the brain. When you do intense squats, the blood flows to your leg muscles so you end up feeling dizzy and lightheaded.
When you go from lying down to a more upright position, such as sitting or standing, if your blood vessels in your legs don't constrict, your blood will remain pooled in your legs and your brain won't get enough oxygen, so again you will feel lightheaded. Blood vessels in legs are supposed to constrict when we stand--when they don't, it is a condition called orthostatic hypotension. It is actually quite common. I don't think there is anything abnormal with you. You just need to take deep breaths when doing intense squat workouts so your brain gets enough oxygen. You also need to give your body time to adjust when you sit or stand upright. I actually think most adults need to do this and can't suddenly get up from a lying down position.
If you are feeling really lightheaded (like you are about to faint), a quick fix is to get your head lower than your legs so blood will flow downhill to your brain. You can do this by lying down with your legs propped up on something.