I don't know if it's normal to have lightheadedness when you aren't feeling anxious. I do however, have constant dizziness and headaches, even when I'm not anxious and I hate it. I have suspected sinuses and whatnot, but I haven't been to the doctor yet, even though I know I should go. I just hate going so much because I feel like I'm a hypochondriac, and that it's all in my head.
I have also had a couple of what I think are vertigo spells. One thing I think I've noticed is that perhaps it's anticipatory or something. I feel like if I think about it, it makes it worse. I am going to go to the doctor, or at least give him a call to see what he thinks, but I think it's possible that I am just being overanalytical, as usual.
Maybe you should give your doctor a call at the very least. Also, have you been put on any meds that could be making you feel lightheaded? I am on a blood pressure medicine(beta-blocker), Propranolol and it can cause dizziness/lightheadedness. If you are on a med, maybe you should just check and see if it's a side-effect.
Try not to get caught up in the side-effects, though. I do that and I scare myself into thinking I am going to have all the side-effects, and obviously, that causes alot of problems. I hope someone responds to you with a more sure answer. I am not sure and am definitely not a medical professional. One thing to think about too, is if you are on the computer a whole lot, or using electronics constantly, try and lay off.
I came to realize I feel better when I lay off from the games and the computer and my iPhone a bit. Anyways, again I hope someone gives you some good advice, and you can get to the bottom of your problem.
Hugs and God Bless.