I'm stuck with my ship in a game on Arita island, and I'm unable to move it or find a nearby wharf manager. I've tried looking for solutions, but nothing has worked yet. Should I contact support for help? I'm playing on PlayStation and I don't want to abandon my ship or waste any more time on this. Any suggestions on what I should do?

Here's what I'd do if my ship were stuck on Arita Island: 

1. Swim over to Padix Island (it's just to the left of Arita Island).

2. Run northwest across Padix Island to the Barter NPC.

3. Swim across the bay north to Pirate Island.

4. Find the Warf Manager on Pirate Island and remotely collect your ship.

(These steps assume you have an outfit that increases your swim speed and reduces your stamina loss. If you don't have an outfit like this, you shouldn't be out on the ocean anyway.)

Hope this helps!

Or simpler use a travelers map to port to nearest city and remote collect the boat.(if you dont have a map on you you can buy it off mp as long as you have at least 1 marketplace maid)

Also often when boats get stuck its possibile to unstuck em by changing chanell, it wont always work though. 

Have you tried clicking right mouse button over the ship icon? You can teleport the ship to where you want within 40 meters.
Just making sure you know.