Our first cruise (many moons ago) was in mid October, we left port 3 days behind a hurricane. This was on the Sovereign of the Seas, a much older and smaller ship. I felt a little ill the first night , but I still blame the greasy duck I had for dinner and the green cuban cigar I had later. Put Seabands on my wrist and went to bed. Took them off the next day and have never had a problem. My brother and a few of his friends got sick during the trip and we did have significant wave motion. When he remembered his Dramamine, he was fine. The next cruise, he took ginger root and again had no problems until we went out on a 40ft dive boat in 6 foot swells. Again, I think it was more the fact that he ate a heavy greasy breakfast and then was rushing about to get off the ship.
Take Dramamine or ginger root, watch the foods you eat. Avoid greasy or real heavy dishes. You should be fine. The gulf is pretty calm during the late winter and early spring. Wave heights in the gulf right now are between 2 and 5 feet. You won't even notice them.
Relax and forget about it.