aikidojoe

A lot of good advice here.

Breathing I think is the most important one. Not only to exhale on doing the roll (VERY IMPORTANT), but inhaling a deep breath upon getting up. You might want to try some extra aerobic activity and see if that helps.

Stay very hydrated. If you lose 10% of your hydration, your performance drops 50%.

Don't eat large meal before class, but you should eat something (like a banana or apple) about 1.5 hours before class so you still have some energy.

Try focusing on your hands as you go over. To your point of view they are stationary, and by the time you look away, your roll is over and the rest of the world has hopefully stopped spinning (unless of course you were at a bar before class, heh).

I think the best advice I sw here, was to make sure your blood pressure is ok, and not dropping or raising too quickly.

A point not mentioned here is whether or not you're progressing with the technical aspect of the roll. Are you improving? Does it feel better (or rather do you feel less pain when doing and after your roll?) If not, then perhaps you are concentrating on the pain, and that can certainly affect your breathing which affects dizzyness, blood pressure, etc...
Try to get someone a lot higher rank to take the time and see what you might be able to do to improve. You might want to check out a couple videos on ukemi and rolling.

OK, guess I've rambled enough for today. I hope this helps.

Masa Katsu Agatsu