When you move your eyes, your eyes will easily get tired if you move fast. The too tired eye balls will of course cause the eye strain. You will find the dizziness. However it is the temporary symptom. After the little rest, you will get recovery. You could just close your eyes and have the little rest for the recovery.
Well, generally speaking, there are many people who suffer from dizzy eyes when they move their eyes. And we can say that it is kind of normal. And in most cases, dizziness will disappear by itself with time. But if your eyes suffer serious dizzies, I have to tell you that you may have some eye problems, such as uveitis and eye infection. So you should just be careful about them, or it will just make your eyes far from infection resources.