If you are certain your dizziness is not caused by any medical problems, practice your rolling every chance you get. When it seems too difficult, as with anything, return to the basics. Start from seiza, rolling backward and forward. With practice it will get better, but there are two things you can do right now. Remember to breath.
Most beginners hold their breath when they roll.
Rolling for 2 minutes can equate to holding breath for 2 minutes, sure your going to be dizzy. Don't try to do one roll immediately after the other.