Julberry,
Yes, there is a public beach off to the left from the pier. I'm a little fuzzy on the distance of the walk, but I'd estimate it to be 6-8 blocks. I would add, though, that if you have not been to Ocho Rios previously, you might feel uncomfortable walking downtown. There are quite a few locals gathered at the dock that swarm tourists making the walk, trying to sell them items, provide tours, etc, etc, etc. It can be a little intimidating , and from time to time it might be unsafe as well. I would never make the walk alone under any circumstances.
Welcome to the boards.
Ted