Contact form php script sending spam to Gmail - php

Question

I created a php script (for a contact form) to send emails to my Gmail account.
If I use the sender email in the header ($headers = "From: " . $email;), Gmail reports the received message as spam.
If I don't use the email in the header (e.g. the sender name $headers = "From: " . $name;) the message is not reported as spam.
Do you have any suggestion to let me use the email in the header?
Thanks!
<?php
/* Check if the url field is empty (antispam) */
if ($_POST['leaveblank'] != '' or $_POST['dontchange'] != 'http://') {
$name = $_POST['name'];
$faillink = "xxx.php";
header("Location: $faillink");
} else {
$name = $_POST['name'];
$email = $_POST['email'];
$subject_prefix = "[ContactForm]: ";
$subject = $subject_prefix . $_POST['subject'];
$message = $_POST['message'];
$to = "myemail#gmail.com";
$body = "From: " . $name . "\n";
$body .= "Email: " . $email . "\n";
$body .= "Message: " . $message . "\n";
$headers = "From: " . $email;
$oklink = "yyy.php";
$faillink = "xxx.php";
if ( preg_match( "/[\r\n]/", $name ) || preg_match( "/[\r\n]/", $email ) ) {
header("Location: $faillink");
}
$retmail = mail($to, $subject, $body, $headers);
if ($retmail) {
header("Location: $oklink");
} else {
header("Location: $faillink");
}
}
?>

Answer 1

I solved the issue as Iain suggested so I replaced the mail headers as follows:
$headers = "From: " . "noreplay#mydomain.com" . "\r\n";
$headres .= "Reply-To: " . $email . "\r\n";