Trouble on GoDaddy?
Godaddy won’t post a message if its coming from gmail, aol etc, so sending it as the user won’t work. Change:
$headers = "From: $email" . PHP_EOL;
to come from somewhere else, e.g.
$headers = "From: <a href="mailto:email@example.com">firstname.lastname@example.org" . PHP_EOL;</a>