You should be enqueuing your styles using the built-in functionality for loading stylesheets rather than trying to force-print inline styling. If it's for a plugin page, then you should use admin_enqueue_scripts:
function vnm_load_my_css($hook) {
// Check if the passed $hook matches your plugin - no point enqueuing your CSS across all of the admin
if ($hook == 'myplugin') {
// This assumes a path relative to your plugin file; so if your file is in /myplugin/ then your CSS will be in /myplugin/css/
$cssPath = plugin_dir_path(__FILE__) . '/css/';
$cssURI = plugins_url('/css/', __FILE__);
wp_enqueue_style('my-plugin-style', $cssURI . '/mystyles.css');
}
}
add_action('admin_enqueue_scripts', 'vnm_load_my_css', 20, 1);