PHP表单，提交后显示消息

我正在制作一个PHP表单，不知道如何在点击提交并正确验证时让代码显示"消息传递"。这是我迄今为止的代码。我意识到，只要你点击提交，消息就会出现。谢谢你的耐心。

    <?php
// define variables and set to empty values
$nameErr = $emailErr = $genderErr = $websiteErr = "";
$name = $email = $comment = $message = "";
if ($_SERVER["REQUEST_METHOD"] == "POST") {

    if (empty($_POST["name"])) {
     $nameErr = "Name is required";
   } else {
     $name = test_input($_POST["name"]);
   }
   if (empty($_POST["email"])) {
     $emailErr = "Email is required";
   }  else {
     $email = test_input($_POST["email"]);
     // check if e-mail address is well-formed
     if (!filter_var($email, FILTER_VALIDATE_EMAIL)) {
       $emailErr = "Invalid email format"; 
     }
   }
   if (empty($_POST["comment"])) {
     $comment = "";
   } else {
     $comment = test_input($_POST["comment"]);
   }
    if (isset($_POST["submit"])) {
     $message = "Message has been delivered";
   } 

}
function test_input($data) {
   $data = trim($data);
   $data = stripslashes($data);
   $data = htmlspecialchars($data);
   return $data;
}
?>
    <div class="cntr">
    <h2>Contact Form</h2>
<p><span class="error">* required field.</span></p>
<form method="post" action="<?php echo htmlspecialchars($_SERVER["PHP_SELF"]);?>"> 
   <div class="field">
    <label for="name">Name </label>
       <br>
    <input type="text" name="name">
   <span class="error">*<?php echo $nameErr;?></span>
    </div>
    <div class="field">
   <label for="email">Email</label>
        <br>
    <input type="text" name="email">
   <span class="error">* <?php echo $emailErr;?></span>
    </div>
   <div class="field">
    <label for="message">Message</label>
       <br>
    <textarea name="comment" rows="8" cols="40"></textarea>
    </div>
    <button type="submit" class="email" name="submit" value="Submit">Submit</button>
    <?php echo $message; ?><br/> 
</form>
    </div>