Can I get absinthe on a cruise?

I’m going on a Carnival cruise to Cozumel, Mexico, Grand Cayman, Cayman Islands, and Ocho Rios, Jamaica. I want to know if it is possible to purchase a bottle of absinthe with thujone (wormwood extract) in any of these port cities and where (specific stores, etc.). If I can buy it, do I need to sneak it back on the ship? Can I legally bring it into the US?