Was the water especially cold? I've only had this happen in very cold water when swimming without my neoprene cap. I figured it was my ears getting cold inside that messed with my balance.

I think this is pretty common, but not lasting several minutes. I usually notice a moment of dizziness upon exiting the water but only a few seconds.

... or ease off the throttle at the end of the swim and let your heart catch up. If I understand you correctly the problem sounds like when a person "stands up to fast", right? Stephen is right, that's a blood flow issue, so being anaerobic in a prone position might be causing your heart to not be able to keep up with your burly self when you stand up. If you have to slow down the swim right at the end to let your body get ready for the transition and you loose 15-20 seconds but keep your head clear you're still ahead 1 min 40 sec of your previous transition right?

goggles too tight? I loosened mine up a bit and that knocked about half the time off my dizzy spell. the remaining time I attribute to what others have mentioned - vertical to upright too quickly. pausing before getting out of the water was a big help in that respect.

I get a dizzy feeling whenever i swim more than 30min.. Mine is usually gone by the time i reach my towel, but i think there is something to laying off the throttle a little. I always try to fininsh strong and I think the bump in HR might prolong my fog. Funny side note, I swam an hour yesterday which is my longest swim, and towards the end i was trying to figure out what distance i had covered. i knew how many laps, but no matter how i tried to do the math,, nothing.. couldn't do it.. 50 yards a lap. 5280ft in a mile. 3 feet in a yard. nothing.. hilarious to me in the pool. But it made the point evident that my brain wasn't my bodys main concern.