Registering a stylesheet inside my WordPress widget

Please check this reference is_active_widget, check the example for an exact solution. That code will go within the __construct() method right after parent::__construct() is called. wp_enqueue_style works if it is called before wp_head is called. and widget() method are called definitely after wp_head is loaded as it just display the HTML template.

So here is an example of loading scripts for widget.