I'm starting to get this now, I understood all along what you are trying to do but I'm understanding how we need to check this.
First we need to check if the current user is in fact sammy and then run the query if he is or echo You cannot Add New Event is it is not. The key is the first part of that last sentence.
Try this, this will only work is $_SESSION['username'] is set from the login.
PHP Code:
<?php
if ($_SESSION['username']=="sammy")
{
$check1=mysql_query("SELECT * FROM tbllogin WHERE Username='sammy' AND Department='HRAD' AND Permission='True'");
$check2 = mysql_fetch_array($check1);
$username = $check2['Username'];
$dep = $check2['Department'];
$permiss = $check2['Permission'];
echo "$username<br/>$dep<br/>$permiss<br/><br/>";
if($username=="sammy" && $dep=="HRAD" && $permiss=="True"){
$_SESSION['isallowed'] = $check2['Permission'];
?>
<a href="<?=$_SERVER['PHP_SELF'];?>?month=<?=$_GET['month'] . '&day=' . $_GET['day'] . '&year=' . $_GET['year'];?>&v=1&f=true">Add Event</a>
<?php
}
else
{ echo "You cannot Add New Event"; }
?>