put this in your functions.php:
function my_format_artist_links($urls) {
$urls = explode(',', $urls);
$links = array();
foreach ($urls as $url) {
if (empty($url)) continue;
$links[] = '<a href="http://'.$url.'">'.$url.'</a>';
}
return implode(',', $links);
}
and then replace
<p><span>Link(s):</span> <?=$artist_links?></p>
with
<p><span>Link(s):</span> <?php echo my_format_artists_links($artist_links); ?></p>'