Holy moly.
1. Right away you try to use $AccountID without defining it. If it's coming from the original URL, you need to use
$AccountID = $_GET['AccountID'];
2. Next, read about sanitizing user input and SQL injection.
3. All this:
"$_REQUEST["Pool01Name"];
$_REQUEST["Pool02Name"];"
Stuff?
You don't do anything with them the first time, those lines do nothing. Secondly, you should be using an array for this data.
$_Pool01Name = $_REQUEST["Pool01Name"];
$_Pool02Name = $_REQUEST["Pool02Name"]; Should be an array.
4. Your update uses $ContactID, which is also never defined.
5.
if ($query) {
exit;
}
This is the opposite of what you want. You also aren't capturing any MySQL errors to help you.
6. Turn on error reporting!!