Probably use PHP Sessions and add a session variable before the form refreshes, then retrieve it in the next page, show it and delete it.
e.g. in your redirect page
$_SESSION["message"] = "Success!";
then in your forms
if(isset($_SESSION["message"])) {
echo $_SESSION["message"];
unset($_SESSION["message"]);
}
This is the simple way to do it, and I do it like this. You might want to add a global template to your forms so that you can edit the second code globally.
This approach is good if you have different forms and if you redirect to pages that is not the original form, so you can show feedback messages globally.