The "conquer your fears and go for it" line is great advice, and no just bravado--I don't go on many amusement park rides w/ DS because I get feelin' barfy...don't even get me started and that giant viking ship that swings back and forth, totally expected to see breakfast again...so when I took my first cruise it was a 4-day, and same with second. We wore patches behind the ears the first time, had them but didn't use them the second time, have never thought about it since.
Great advice above in going thorugh
DCL directly or a TA that specializes in DCL or at least cruises to identify a date that gives you the best odds (though certainly not a guarantee) of sailing in historically calmer seas.
Most laws are designed to prevent future recurrence of past wrongs. So Titanic is the reason today's cruise ships are safe, not a reason to fear them. I admit--sometimes late in the evening, standing out on deck lookin at the sky and the ocean, and if there isn't a passing ship then there is just darkness, well, yeah, I think back to that movie and forget the movie, the reality of it, and ... I remember all the technology and radar and GPS and sonar and enough motorized, covered lifeboats for all even if there would be a worst case scenario, and I go back to enjoying the stars without the interference of the lights from my city at home.
Go. Get patches/pills, and use them early, not after feeling bad if it happens at all. Get the guidance of a specialist for time of year, location of stateroom help. Watch the DCL show on Travel Channel, or even other cruise shows to learn more about cruising. Start with the shorter duration cruise. Book the second one, for 7 or more days, on board. All set? Enjoy!!