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Definitely sounds like vertigo. As @JimBlay mentioned, with SCUBA this can be caused by a big temperature difference in your ears, but a common cause has to do with little crystals found in the inner ear getting into the wrong places. Fortunately I've never had vertigo in the water, but did experience it at home for the first time just a few weeks ago. I remember very suddenly rolling over in bed to turn off the alarm clock, and all of sudden the room started to spin like crazy. I felt very nauseous and could barely sit up. After a few minutes it subsided, but I had to be very careful about rolling onto my left side or leaning over with my head down for more than a week or the spins and nausea would quickly come back.
My wife experienced this a few years ago, and remembered something called the Epley maneuver - Wikipedia. It involves systematically bending and rotating your body and head to use gravity to move particles in the inner ear away from the sensitive spots. There are some decent YouTube videos demonstrating it.
It looks like voodoo, but my wife insisted I try it and I haven't had any bouts with vertigo since. The vertigo was so bad that I might very well have drowned if I had an attack under water. It was paralyzing.
If you have any relapses out of the water I suggest you try the Epley and/or see a doctor.
@BoundForElsewhere I think you're the first person ever to recognize my avatar.