I too suffer from car sickness...you almost wish you could just die!!!
I have been on 2 cruises and will also be going on the Carnival Spirit to Alaska in May 2006, and so far I have not had any sea sickness. I do take Antivert, twice a day. Car or sea sickness is caused by an inner ear inbalance. I would just about bet that this is your problem, and I think that inner ear problems are more common in some families. I know that my mother, aunt, grandmother, and myself all suffer from inner ear problems. We can't ride in the back seat of a car or heaven forbid read a book!
The only time I had any dizziness on a cruise, was when I was sitting near a window eating breakfast one morning. Got just a little queasy, but after I went up on deck in the fresh air, I was fine.
Talk to your physician and see if they will write you a pres. for Antivert. Take it a couple of days before your trip, and then while you're cruising, you should be fine.