How to display an admin notice after updating plugin settings?

I have a plugin with a setting page, and there are some action that have to be done when a certain option is saved. I am using the pre_update_option_ hook to do this. So far so good. If something goes wrong, however, I’d also need to notify that to the user.
I tried these things:

1) Add hook to admin_notices before updating the code

add_action ('pre_update_option_my_var', function( $new_value, $old_value) {
    //Do my validation
    $valid = ( 'correct_value' == $new_value );

    if ( !$valid ) add_action('admin_notices', 'my_notification_function' )
    return ($valid)? $new_value : $old_value;
});

The validation works, but the notification is not displayed because, I assume, by then the functions hooked to admin_notices have already been executed?

2) Validation in the function hooked to admin_notices
To solve the problem above, I had this idea.

add_action('admin_notices', function () {

      //Do my validation
      $valid = ( 'correct_value' == $_POST['my_var'] );
      if (!$valid) { /* Display error message */ }
      //Store the value of $valid
});

add_action ('pre_update_option_my_var', function( $new_value, $old_value) {
    //fetch the value of $valid which I stored 
    return ($valid)? $new_value : $old_value;
});

Now, this would seem to work well, I do see the notification now. The problem is that for some strange reason I don’t see the posted values. I tried to print $_POST and it always empty! Probably WordPress is passing the values in some other way? If so, how?

Which one is the right way to go, and how can I fix the issue? Of course, if any other method is better than these two and solves the issue, it’s welcome.

After digging in the setting API I found the answer. Method 1 was correct, but the notification should not be done by hooking to admin_notices, rather by the function add_settings_error

add_action ('pre_update_option_my_var', function( $new_value, $old_value) {
    //Do my validation
    $valid = ( 'correct_value' == $new_value );

    if ( !$valid ) {
         //This fixes the issue
         add_settings_error( 'my_var', $error_code, $message );
    }
    return ($valid)? $new_value : $old_value;
});

In order to display them, this also needs to be added at the beginning of the settings page:

<h2>The heading of my settings page</h2>
<?php settings_errors(); ?>