Shortcode from a function not working

If you refer to the documentation for add_shortcode, you need your function to return the content:

function uniquetestfunction($attributes) {
   return '<div class="my_class">Test Element</div>';
}
add_shortcode('uniqueshortcodename','uniquetestfunction');

You also used the wrong quotes in your add_shortcode line – stick with single ' or double " quotes.