Green tea makes me dizzy?!
Green tea does contain caffeine, not as much as an equal amount of coffee, but as much as black tea, depending on the brand, anywhere between 15 to 75 milligrams per 12 ounce serving. And it also increases the body's metabolism. I'd strongly suggest you avoid drinking it.
Green tea has caffine(if it's not decaf i think). it has a lot more caffine than coffee in its dry form. I suggest stop drinking this.
Try this site; http://en.wikipedia.org/wiki/Green_tea#Caffeine
All tea (except some herbal "teas") contain caffeine. even decaf. Decaffeinated does not mean caffeine free.
Then don't drink green tea.