Can’t get only one links category in sidebar

I am trying to make a page of links using Links Manager but not have that category show in the sidebar.

I am having difficulty getting the second category of links (my favorite links) out of the sidebar
blog is here https://www.amber438.com
I want to keep the blogroll on the sidebar. been working on this for hours
code I am using is as follows:

<?php
$link_cats = $wpdb->get_results(“SELECT cat_id, cat_name FROM $wpdb->linkcategories”);
foreach ($link_cats as $link_cat) {
?>
<li id=”linkcat-<?php echo $link_cat->cat_id; ?>”><h2><?php echo $link_cat->cat_name; ?></h2>

<?php wp_get_links(1); ?>

<?php } ?>

I’m a newb so there is probably a simple solution I have not found yet
Thanks!!!