Remember that time I tried to take a picture of a hawk? I was so focused on keeping still and waiting for the perfect pose, I totally forgot to breathe normally. Next thing I know, my vision got all spotty right as it took off. I missed the shot completely because I was seeing stars instead of the bird! It's crazy how easy it is to get locked in and mess up the simple stuff when you're concentrating.
My buddy did something similar trying to film a woodpecker. He was so locked on the viewfinder, holding his breath for like a full minute. When the bird finally moved, he stood up way too fast and just fell over sideways into a bush. Had a scratch on his cheek for a week. We still give him grief about it.
Deep breathing shouldn't make you that dizzy unless you were doing it totally wrong. Sounds like you might have just been holding your breath waiting for the shot.