You need a semicolon after your echo statement:
{echo "<td>Booked By ".$row['Username']."</td>";}
Errors like this might be easier to find if you adopted a clearer block/indent style. Your code is pretty hard to read.
For example:
for ($period=1; $period<6; $period++)
{
echo "<tr><td>".$period."</td>";
for ($room=0; $room<sizeof($rooms_array); $room++)
{
$sql = "SELECT Username FROM Booking WHERE RoomID ='".$rooms_array[$room]."' AND Period = '".$period."' AND Date = '".$sentdate."'";
$result= sqlite_query($con,$sql);
$row = sqlite_fetch_array($result);
if($row['Username']==$_SESSION['Username'])
{
echo "<td>Booked By ".$row['Username']."</td>";
}
}
}