Change localization only for plugin

Use plugin_locale filter:

apply_filters( 'plugin_locale', $locale, $domain );

Change locale like this:

$my_plugin_domain = 'my_plugin_domain_name';
$override_locale="es-ES";
add_filter('plugin_locale',
    function ($locale, $domain) use ($my_plugin_domain, $override_locale) {
        if($domain == $my_plugin_domain) {
            $locale =  $override_locale;
        }
        return $locale;
    }, 10, 2);