i don't know when you leave...but about 24 hours before you go start taking dramamine as directed on the bottle (if not allergic) so it's in your system when the boat starts rocking. or try a scopolamine patch (goes behind your ear like a small bandaid, and again, if not allergic)
don't look over the edge.
don't fall over.
the pools are shallow and the hot tubs are as well. but if unsure you can always lounge on the deck or on the beach. or find something to do onboard. as they say "at any one time there are a million ways to have fun."
i think you will be fine, but that does not mean i am discoursing your concern. remember it is still a ship although it feels like a small town, follow the safety guidelines, get some seasickness medicine and you should be ok.
there is an infirmary on board if you really need it.
i have never been disappointed on a cruise...i just came off my 6th. i hope you have the time of your life!