Just build an "if" check around the form, no need to redirect at all.
First you should set a variable or something if the mail has been successfully sent:
PHP Code:
if (mail(...blah)) {
$success = yes;
}
Then around the actual <form> elements in the page you should do something like:
PHP Code:
<?php
if (!isset($success)) {
// Break out of PHP and show the form:
?>
<form.... blah blah>
Insert your form mumbo jumbo.
</form>
<?php
}
else {
echo "Thanks for contacting us. Blah blah blah";
}
?>