I'm building a simple contact form for a website. It does not connect to a database, it just sends the email. Will this code prevent spammers from using header injections? Are there any vulnerabilities I'm not seeing?

//create short variable names
$name= filter_var($_POST['Name'],FILTER_SANITIZE_STRING);
$email= filter_var($_POST['Email'],FILTER_SANITIZE_STRING, FILTER_VALIDATE_EMAIL);
$subject= filter_var($_POST['Subject'],FILTER_SANITIZE_STRING);
$message= filter_var($_POST['Message'],FILTER_SANITIZE_STRING);

//set up some static information
$toaddress = '[email protected],[email protected]';

$mailcontent = "Customer name: ".$name."\n".
            "Customer email: ".$email."\n".
            "Subject: ".$subject."\n\n".
            $message;

$fromaddress = "From:" . $email;

//invoke mail() function to send mail
mail($toaddress, "Website Contact Form",$mailcontent, $fromaddress);
?>