Is it normal to get light headed when doing pull-ups?

It might be if you aren't hydrated or haven't eaten well earlier in the day. If you are inadvertently holding your breath, it could happen. Why not have the gym trainer evaluate your form? Maybe, do three, rest, then two more sets of three to build your strength. Have a friend video tape your form and show a trainer. Your lungs may not be able to hold enough oxygen just yet, or maybe you are working out at a geographical area way above sea level where there is less oxygen. That might be causing a problem.