You cant call a shortcode inside a shortcode they do not automatically nest, you need to use do_shortcode($content) like this (i am assuming the name of your shortcode):
function alert_shortcode( $atts, $content = null ) {
return '<div class="alert alert-' . $atts['type'] . '" role="alert"><p class="alert-title">' . $atts['title'] . '</p>' . do_shortcode($content) . '</div>';
}