It is hard to say what you need to hook into without knowing all the details but I think you may be able to use comment_text
— more or less the the_content
of comments.
add_filter(
'comment_text',
function ($comment) {
return $comment.'<div>This is your special division</div>';
}
);
If that isn’t quite right, take a look at the filters listed in the Codex for comments.