You would probably want to create a development environment on a subdomain, but if you are restricted by this, you will want to enqueue the style only when you are logged in.
In style.css (change twenty fourteen to match your current theme)
/*
Theme Name: Twenty Fourteen Child
Theme URI: http://example.com/twenty-fourteen-child/
Template: twentyfourteen
*/
@import url("../twentyfourteen/style.css");
In header.php
if ( is_user_logged_in() ) {
if ( $user_id = YOUR_USER_ID ) {
wp_register_style('YOUR_STYLE', get_stylesheet_directory_uri() . 'PATH.css');
wp_enqueue_style('YOUR_STYLE');
}
}
This should be the general idea of what you want to do. Comment if you have any questions.