How to sort list of custom posts to get view like a tree of posts under categories and their children’s categories?

I’m new here and my english isn’t perfect so I’m sorry for this 🙂 I’m here because I’m workin on site with post list sorted by category and I have problem with sort out my posts in categories and children categories under them. Now everything is messed up. I would like to sort my custom posts like that:

CATEGORY 1

• CHILD CATEGORY 1

  • Post
  • Post
  • Post

• CHILD CATEGORY2

  • Post
  • Post
  • Post

CATEGORY 2

• CHILD CATEGORY3
  • Post
  • Post
  • Post

CATEGORY 3

• Post

• Post

• CHILD CATEGORY4

  • Post
  • Post
  • Post

Is it possible with this code:

<?php
$querystr = "SELECT terms.* FROM $wpdb->term_taxonomy tax LEFT JOIN $wpdb->terms terms ON       tax.term_id = terms.term_id WHERE tax.taxonomy = 'MY_CUSTOM_TAXONOMY'";

$categories = $wpdb->get_results($querystr, OBJECT);

foreach( $categories as $category ): 
echo '<div class="category-header"><h3>'.$category->name.'</h3>';  
echo '<p class="category-description">'.strip_tags(term_description($category->term_id,'MY_CUSTOM_TAXONOMY')).'</p></div>';  

$posts = get_posts( array( 'MY_CUSTOM_TAXONOMY' => $category->name, 'post_type' => 'MY_CUSTOM_POST' ) );  
foreach($posts as $post) :  
setup_postdata($post);  

 the_title();   

endforeach;

endforeach;
?>

I will be grateful for all help, thank You!!

ok, this is my working solution:

<?php

$args=array(
'post_type'                => 'biblioteka',
'child_of'                 => 0,
'parent'                   => '',
'orderby'                  => 'name',
'order'                    => 'ASC',
'hide_empty'               => 1,
'hierarchical'             => 1,
'exclude'                  => '',
'include'                  => '',
'number'                   => '',
'taxonomy'                 => 'kategoria-pozycji',
'pad_counts'               => false
);

$categories=get_categories($args);

foreach ( $categories as $category ) {

if ( $category->parent > 0 ) {
continue;   
}

echo '<h1 style="font-weight:bold">' . $category->name . '</h1>';

$querystr = "SELECT $wpdb->posts.*
          FROM $wpdb->posts, $wpdb->term_relationships, $wpdb->terms
          WHERE term_id = (" . $category->cat_ID . ")
          AND term_taxonomy_id = (" . $category->term_taxonomy_id . ")
          AND ID = object_id
          AND post_type="biblioteka"
          AND post_status="publish"
          ORDER BY post_date DESC";
$posts = $wpdb->get_results($querystr, OBJECT);

echo '<ul>';
foreach ( $posts as $post ) {
    setup_postdata($post);  

        echo '<li>'; the_title();   echo '</li>';

        }
echo '</ul>';

$categories2 = get_terms('kategoria-pozycji',array('parent' => $category->term_id , 'hide_empty'=> '0' ));

foreach ( $categories2 as $category ) {

echo '<h2>' . $category->name . '</h2>';

$posts = get_posts( array( 'kategoria-pozycji' => $category->name, 'post_type' => 'biblioteka' ) );  

echo '<ul>';
foreach($posts as $post) { 
    setup_postdata($post);  

        echo '<li>'; the_title();   echo '</li>';

        }
echo '</ul>';

}
}

?>