Menu Item Location

The wp_nav_menu_items filter has a secondary parameter that it passes: $args. What we need to do is set up our filter to accept second args by passing a priority 10 and the number of args 2:

add_filter( 'wp_nav_menu_items', 'my_counter_nav_menu', 10, 2 );

Now that we’re passing args – if we peek into what it holds we see the following object:

stdClass Object
(
    [menu] => Menu Name
    [container] => nav
    [container_class] => 
    [container_id] => mainNav
    [menu_class] => menu
    [menu_id] => 
    [echo] => 1
    [fallback_cb] => wp_page_menu
    [before] => 
    [after] => 
    [link_before] => 
    [link_after] => 
    [items_wrap] => <ul id="%1$s" class="%2$s">%3$s</ul>
    [depth] => 0
    [walker] => 
    [theme_location] => 
)

So if we wanted to in your function we can test against either $args->menu or $args->theme_location:

if( 'Menu Name' === $args->menu ) {
    /* .. Run Code Here .. */
}

Or against the location:

if( 'primary-menu' === $args->theme_location ) {
    /* .. Run Code Here .. */
}