Rearranging Content After Blog Post

If editing the theme files, chances are you want to place your custom block of code right after a line of code that might look something like:
<?php get_template_part( 'content/entry' ); ?>

It should also be before any call to the function comments_template() if you want it to show before the comments.

You mention using a plugin called Facebook Comment Plugin. I don’t have any experience with this plugin, but ideally, it would tap into the comments_template function rather than try to filter itself earlier.

Depending on the theme you are using, you may have actions you can tap into that can add your custom block of code. Using actions is the best option if actions are available.

In a worst-case scenario, you could use a filter to add your content block to the end of the actual post content:

function my_author_box($content) {
    if (!is_feed()) {
        $authorbox = '<p>This is my authorbox code....</p>';
        $content = $content . $authorbox;
    }
    return $content;
}
add_filter('the_content', 'my_author_box');

Again, this previous sample would be added into your functions.php file or into a custom plugin, but I would recommend only doing this as a last resort as filtering the_content applies your code in more places than you might expect or want it to.