Try to add date_query
to the $qry in the solution mentioned here.
$qry = new WP_Query(
array(
'cat' => $current_post_categories[0],
'posts_per_page' => 2,
'post__not_in' => array( $current_post_id ),
'date_query' => array(
array(
'before' => $post->post_date,
),
),
));