API Hook for After Commenting (for sharing on Facebook)

Have you tried comment_post action? It’s fired right after the comment is inserted into the database.

function share_comment_on_facebook( $comment_ID ) {
    $commentdata = get_comment( $comment_ID );

    if ( $commentdata['comment_approved'] ) {
        // fire up the code to launch pop up
    }
}
add_action( 'comment_post', 'share_comment_on_facebook' );