I don't know enough about this to be a real help, but if you want to output HTML in the message body, you have to specify that. So try adding a fourth $headers part to the mail() function and include something like this:
$header = "Content-Type: text/html; charset=UTF-8;\\r\
mail($email, 'Changes', $message, $header);
Also, try removing those quotes around the variables in the mail() function.