How to change a meta value (of a published post) after X days.?

You shouldn’t need to use a meta field for this logic.

In the loop $post->post_date holds when the post is published. From there you can determine if the date is 90 days old:

$datetime = strtotime($post->post_date);
if( $datetime < ( time() - ( 60 * 60 * 24 * 90 ) ) ) {
    echo "> 90 days old"
} else {
    echo "< 90 days old"
}