@Faintdreams I'm still learning about the geology of Jamaica but from what I understand it's a combination of those. 140+ million years ago*, there was no Jamaica because there was no ocean in between Europe/North America and Africa/South America. When that supercontinent started splitting apart, there was plenty of volcanic activity, and the rocks that formed from that are part of Jamaica, but part of it is also pieces of that old continent. So it is mountainous but also pretty old. And, a large part of the land there is made of limestone, which is highly erodible, so that may contribute to the preponderance of sand as well. Just speculating about that last part though.
*edited to correct myself: the supercontinent (Pangaea, which you may have heard of) existed 300 million years ago and its breakup lasted from 150 - 100 million years ago. I initially put that breakup at 50 million years ago, but I was getting the Pangaean breakup confused with the collision of the Caribbean plate with the north American plate which took place about 50 million years ago, and which really put Jamaica into something resembling its current form.
I love geology! Please continue with the questions if you have more.