How do I stop my blog from pinging back itself?

You could try this by putting code in functions.php in your theme.

function no_self_ping( &$links ) {
$home = get_option( 'home' );
foreach ( $links as $l => $link )
    if ( 0 === strpos( $link, $home ) )
        unset($links[$l]);
}
add_action( 'pre_ping', 'no_self_ping' );

Hope this helpful to you.