Maybe you're just not in good enough shape to do that level of effort.

Eventually your cardiovascular system is so strong that your legs can't keep up and this won't happen anymore unless you just go super crazy, at which point, yeah, it's normal to feel dizzy, breathe heavy and see spots. Because that's what happens when you raise your heart rate to the limit.

Track your HR while this happens and see if it's something crazy like 90-95% of your max. If you get this while at 70-85%( or less) then maybe that's trouble, I dunno.