Ok I got it. If anyone is wondering, you need to create $where between the two dates:
$where .= " AND post_date >= '" . date('Y-m-d', strtotime('+1 day')) . "'" . " AND post_date <= '" . date('Y-m-d', strtotime('+7 days')) . "'";
And it works.
Any help on this? I am on deadline here.