Without plugins, you could do this:
- Create a page template with the HTML you want to appear before or after the form (you can copy your page.php as a start. You can prefix that custom html with a call for
if (is_user_logged_in()):
so it only appears to logged in users. Make sure the the_content();
call happens where you want the form to appear.
- Edit the page where you have the form. Make sure the proper shortcode is in the content. Change the template to the template you just created.