shortcode – I need to throw a message or load a different page

Move your form processing code outside the shortcode so you can hook it to an earlier action before headers are sent, then you can do whatever redirection you need to after the form is processed.

function process_int_form(){
    if ( isset( $_REQUEST['int_prefix'] ) && isset( $_REQUEST['int_suffix'] ) ) {
        // process form
        wp_redirect( home_url( $_SERVER['REQUEST_URI'] ) );
    }
}
add_action( 'init', 'process_int_form' );