I have suffered from anxiety/panic attacks for 15 years. The constant dizziness/lightheadedness is something that is very common and can happen anywhere, at anytime, anxious or not. There was a time period when I had to hold on to stuff to keep from falling over...this lasted 3 months!! Sometimes there is just a constant lightheadedness....it worsens with hormones, so usually it's worse when I'm pregnant, nursing, or pmsing.
You are not alone and it is normal. Mine was so bad I even had 2 brain mri's and trip to the ENT. Normal.
There is a site that has helped me immensely...it is
www.nomorepanic.co.uk