Email not received

Question

I've created a contact form and am sending an email on submission. Once submitted, I get the 'success' message. however, when I check my email, the message doesn't reach my mailbox.

Here is the form:

<form name="sentMessage" id="contactForm" novalidate="">
<div class="row">
    <div class="col-md-6">
        <div class="form-group">
            <input type="text" class="form-control" placeholder="Your Name *" id="name" required="" data-validation-required-message="Please enter your name." aria-invalid="false">
            <p class="help-block text-danger"></p>
        </div>
        <div class="form-group">
            <input type="email" class="form-control" placeholder="Your Email *" id="email" required="" data-validation-required-message="Please enter your email address.">
            <p class="help-block text-danger"></p>
        </div>
        <div class="form-group">
            <input type="tel" class="form-control" placeholder="Your Phone *" id="phone" required="" data-validation-required-message="Please enter your phone number.">
            <p class="help-block text-danger"></p>
        </div>
    </div>
    <div class="col-md-6">
        <div class="form-group">
            <textarea class="form-control" placeholder="Your Message *" id="message" required="" data-validation-required-message="Please enter a message."></textarea>
            <p class="help-block text-danger"></p>
        </div>
    </div>
    <div class="clearfix"></div>
    <div class="col-lg-12 text-center">
        <div id="success"></div>
        <button type="submit" class="btn btn-xl">Send Message</button>
    </div>
</div>

contact-me.js:

// Contact Form Scripts

$(function() {

    $("#contactForm input,#contactForm textarea").jqBootstrapValidation({
        preventSubmit: true,
        submitError: function($form, event, errors) {
            // additional error messages or events
        },
        submitSuccess: function($form, event) {
            event.preventDefault(); // prevent default submit behaviour
            // get values from FORM
            var name = $("input#name").val();
            var email = $("input#email").val();
            var phone = $("input#phone").val();
            var message = $("textarea#message").val();
            var firstName = name; // For Success/Failure Message
            // Check for white space in name for Success/Fail message
            if (firstName.indexOf(' ') >= 0) {
                firstName = name.split(' ').slice(0, -1).join(' ');
            }
            $.ajax({
                url: "././mail/contact_me.php",
                type: "POST",
                data: {
                    name: name,
                    phone: phone,
                    email: email,
                    message: message
                },
                cache: false,
                success: function() {
                    // Success message
                    $('#success').html("<div class='alert alert-success'>");
                    $('#success > .alert-success').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                        .append("</button>");
                    $('#success > .alert-success')
                        .append("<strong>Your message has been sent. </strong>");
                    $('#success > .alert-success')
                        .append('</div>');

                    //clear all fields
                    $('#contactForm').trigger("reset");
                },
                error: function() {
                    // Fail message
                    $('#success').html("<div class='alert alert-danger'>");
                    $('#success > .alert-danger').html("<button type='button' class='close' data-dismiss='alert' aria-hidden='true'>&times;")
                        .append("</button>");
                    $('#success > .alert-danger').append("<strong>Sorry " + firstName + ", it seems that our mail server is not responding. Please try again later!");
                    $('#success > .alert-danger').append('</div>');
                    //clear all fields
                    $('#contactForm').trigger("reset");
                },
            });
        },
        filter: function() {
            return $(this).is(":visible");
        },
    });

    $("a[data-toggle=\"tab\"]").click(function(e) {
        e.preventDefault();
        $(this).tab("show");
    });
});


/*When clicking on Full hide fail/success boxes */
$('#name').focus(function() {
    $('#success').html('');
});

contact-me.php:

<?php
// Check for empty fields
if(empty($_POST['name'])      ||
   empty($_POST['email'])     ||
   empty($_POST['phone'])     ||
   empty($_POST['message'])   ||
   !filter_var($_POST['email'],FILTER_VALIDATE_EMAIL))
   {
   echo "No arguments Provided!";
   return false;
   }

$name = strip_tags(htmlspecialchars($_POST['name']));
$email_address = strip_tags(htmlspecialchars($_POST['email']));
$phone = strip_tags(htmlspecialchars($_POST['phone']));
$message = strip_tags(htmlspecialchars($_POST['message']));

// Create the email and send the message
$to = 'yourname@yourdomain.com'; // Add your email address inbetween the '' replacing yourname@yourdomain.com - This is where the form will send a message to.
$email_subject = "Website Contact Form:  $name";
$email_body = "You have received a new message from your website contact form.\n\n"."Here are the details:\n\nName: $name\n\nEmail: $email_address\n\nPhone: $phone\n\nMessage:\n$message";
$headers = "From: noreply@yourdomain.com\n"; // This is the email address the generated message will be from. We recommend using something like noreply@yourdomain.com.
$headers .= "Reply-To: $email_address";
mail($to,$email_subject,$email_body,$headers);
return true;
?>

I'm not too sure what is going wrong here, it my just be the server config that might be causing the issue.

Could anyone see where/what I'm going/doing wrong?