Not breathing enough, or drinking enough, would tend to make you lightheaded (going to pass out feeling, like from jumping up from the sofa too fast), but not dizzy (room is spinning feeling). I think the dizziness that comes from repeated rolling on one side is from stimulation of sensors in the ear.
My first sensei would say to alternate rolls (left-right-left-etc) to avoid this, and it worked for me. Then I hit a dojo that required small forward rolls, one side, length of mat. What finally got me over the dizziness was doing several lengths
of the mat, every day. I hit upon this when the instructor who anted one length noticed how dizzy I was and told us to do two, instead. Part of me thought he might just be sadistic
, but part of me figured he might know something I didn't.
I have a couple of theories on why it helped me over my dizziness: it might be that I just learned to supress what my semicircular canals are telling me, or it could be in the beginning I had my head tilted in a bad way or moved it around too much, and with continued practice (kind of the 'thousand bokken cuts' theory) I found the right place to put it and trained that in...or a combination.
But the good news is, it did stop.