Post Templates and Post ID’s

But for some reason my posts get overridden instead of displaying new
data.

The problem is here: $announcements->query('showposts=1&cat=$category_id');

You are trying to use a variable inside a single quote string. Variables do not expand inside single quotes so instead of asking for cat=1, or cat=2, you are literally asking for cat=$category_id— just like that, spelled out in full.

What you need instead are double quotes: $announcements->query("showposts=1&cat=$category_id");. Variables do expand in double quote.

Or better, an array– far more readable and maintainable:

$args = array(
  'posts_per_page' => 1,
  'cat' => $category_id,
);

Note: showposts is deprecated. Use posts_per_page.