How could I create a ‘private comments’ section on a custom post type?

Comments have an associated author to them.

In a section called “Private Comments” – Query for all comments belonging to the current post where wp_comments->comment_author_email equals the email of the current user.

Checkout the wp_comments table. It has 15 or so fields you can filter when displaying comments.

EDIT:
The code would look something like this:

 $comment_array = get_approved_comments($post->ID);

 $current_user = wp_get_current_user();

   foreach($comment_array as $comment){
      if ($comment->comment_author_email == $current_user->user_email) {
              echo $comment->comment_content ;
      }

   }

You loop through the list of comments for the current post and filter by author email.