If you don't have reservations, make sure you get to Caye Caulker as early in the day as possible, before noon preferably. The island has approx. 300 rooms, and if it is filled up, yes, you will be left out in the cold (or the sand) www.staycayecaulker.com
is a booking agent for many hotels, I would have at least my first night's reservations taken care of. The island is quite busy now and will get even busier the closer you get to Easter.