Sea Calm/Bonine/Meclizine is not really a remedy. It's really a preventative. It might not stay down, if you wait to take it until you already feel seasick. We take one the day before we sail and each day while the sea is calm at breakfast..twice a day if it's not. It's not supposed to make you as sleepy, however it does a little for me. Also, if you drink alcohol, it seems to make you sleepier, or so I've been told. I also have to take it the day after my cruise, since I have a problem once back on shore.
This is our first time on a Dis cruise, but on all others, it has always been available at the infirmary and pursers desk. If you say you have asthma, they won't (or shouldn't) give it to you without a doctor visit.