You really need to have administrator rights to do any type of real troubleshooting on the server.
However, if you want to figure out if it is your code or the server's fault (heh), there are a few steps you can take. One of them is to add a timer to your php code to see how long it is taking to execute on the server. From here:
<!-- put this at the top of the page -->
<?php
$mtime = microtime();
$mtime = explode(' ', $mtime);
$mtime = $mtime[1] + $mtime[0];
$starttime = $mtime;
?>
<!-- put other code and html in here -->
<!-- put this code at the bottom of the page -->
<?php
$mtime = microtime();
$mtime = explode(" ", $mtime);
$mtime = $mtime[1] + $mtime[0];
$endtime = $mtime;
$totaltime = ($endtime - $starttime);
echo 'This page was created in ' .$totaltime. ' seconds.';
?>
Using this, you can see if the server is actually slow, or if it is on the connection end.
If the server is slow there are a number of steps to take but you need admin rights to go any further, especially since you are using wordpress which is on hundreds of thousands of servers worldwide and is fairly optimized.
One more thing to try is to disable plugins and enable them one by one to see if any are causing your slowness.