<?php
$query = mysql_query("SELECT * FROM Items WHERE Owner='{$User['ID']}', Class='{$Equipping['Class']}', Equipped='Yes'");
$rows = mysql_num_row($query);
if ($rows > 0) {
print "You already have ".$Equipping['Class']." equipped!";
}
?>
$User[ID] will not parse in your syntax. Use { }.
Your query was incorrect, thus your $CheckClass1 was not a result, hence (uf!) $CheckClass was throwing an exception. (you can see how an erroneous query can have a domino effect).
Also, apply some standard naming while at it and make a habit of naming varibles like this: User['ID'].