Search result based on URL

You don’t and shouldn’t rely on referrers ( they can be stripped, hidden, or just outright lies )

Instead there are alternatives

such as submitting to the post type archive:

<form action="/courses" method="get">
    <input type="test" name="s"/>
</form>

Or bundling query vars as hidden inputs:

<form action="" method="get">
    <input type="test" name="s"/>
    <input type="hidden" name="post_type" value="course" />
</form>

Or even just:

mywebsite.com/?s=foo&post_type=course

etc