wp_login action hook not working

I have spent many time looking for a solution to my issue, but in vain. Your help is invaluable.

I am creating a simplified badge system. The goal is to increment the number of badges for a user if he performs some things on the website. For example, for each post published, I give a user one badge.

To do so, I opted for user meta data, and the use of publish_post action hook.

in my functions.php, I put:

function publish_badge($post_ID) {

   global $current_user; 
   get_currentuserinfo();

   $number_of_badges = get_user_meta($current_user->id,'user_number_of_badges',true);
   $number_of_badges = $number_of_badges + 1;
   update_user_meta($current_user->id, 'user_number_of_badges', $number_of_badges);
   return $post_ID;             
}
add_action('publish_post', 'publish_badge');

I am new in using WordPress action hooks, and I spent a lot of time making it work. I know I am missing something, since for other hooks, the problem remains.

Note I have in total 4 actions for which I want to give users more badges: publish_post,edit_post,wp_login,comment_post.

Your usual help is always appreciated.

Edit:

I found solution for all the hooks except wp_login, In fact, I am using custom post types so I should change my hook names.
in other words, publish_post will become publish_cpt.

What to do with wp_login??

    function login_badge($user_login) {
    global $current_user; 

    get_currentuserinfo();
 $number_of_badges= get_user_meta($current_user->id,'user_number_of_badges2',true);
   $number_of_badges= $number_of_badges +5;

  update_user_meta($current_user->id, 'user_number_of_badges2', $number_of_badges);

    }


add_action('wp_login', 'login_badge');

thank you for your time.