For the past ten days in a row, I have not been able to sleep. This morning when I woke up and started walking around, I felt really lightheaded. I know what fainting feels like and it was kind if similar to that. I was just wondering if this was normal. I thought maybe it might be because of my lack of sleep but I'm just not sure.

We can't be sure either, and if you really suddenly aren't sleeping, you need to see a doctor.
'I can't sleep' rarely means that literally. You would be hallucinating after about 4 days with no sleep.
If you want, say more about your age, gender, history, general health, anything you take, and changes in your life.

One very preliminary question: do you drink enough fluids?

Ok well I'm 13... a girl and I do drink enough fluids. I went to see a therapist about me not being able to sleep, and apparently its about anxiety. But all I am really wondering is why I feel light headed all of the sudden and if it is linked to this.

Sure, it can be linked to anxiety and not enough sleep, or any number of things.
I see other posts you have written about some problems with best friends, and that might all be what is causing the inability to sleep and the anxiety and the lightheadedness.

Worries are things we have all throughout life in varying degrees, and how we deal with them is what determines whether we can call ourselves healthy. (I'm not including victims of attack, political oppression, war, starvation, witnesses to murder and horror, and other such events.)

Your therapist will help you learn how to get through anxious times. It's good that you are going. I had therapy (not as young as you) and the one big thing I learned that is simple but very hard to put into practice is that no one 'makes' us do anything unless they physically force us. We feel the way we do because we allow others to affect us, not because they 'made' us feel that way. This can take a lifetime to work on. Good luck.