Ok, i will help you with the logic of the first part.
if you are on page artwork-details.php?id=2, for example, we want to go to
artwork-details.php?id=1 if the user clicks prev,
artwork-details.php?id=3 if the user clicks next.
so, your link code for the next link could look something like this...
<a href="artwork-details.php?id=<?php echo isset($_GET['id'])?$_GET['id'] + 1:1;?>">
the php goes like this. if the get parameter is set, add one to it, then echo this value, otherwise echo the value 1
so the link will always point to the record whose id is one higher than the current one, and if there is no id set, it will point to the first record