How can you check if you are in a particular page in the WP Admin section? For example how can I check if I am in the Users > Your Profile page?

The way to do this is to use the ‘admin_enqueue_scripts’ hook to en-queue the files you need. This hook will get passed a $hook_suffix that relates to the current page that is loaded:

function my_admin_enqueue($hook_suffix) {
    if($hook_suffix == 'appearance_page_theme-options') {
        wp_enqueue_script('my-theme-settings', get_template_directory_uri() . '/js/theme-settings.js', array('jquery'));
        wp_enqueue_style('my-theme-settings', get_template_directory_uri() . '/styles/theme-settings.css');
        ?>
        <script type="text/javascript">
        //<![CDATA[
        var template_directory = '<?php echo get_template_directory_uri() ?>';
        //]]>
        </script>
        <?php
    }
}
add_action('admin_enqueue_scripts', 'my_admin_enqueue');