This thread is resolved. Here is a description of the problem and solution.
Problem: I am trying to add category label to my translated posts. I have a PHP function that display label before post title. It works fine with default language (Polish), but do not work with their translation into English.
Solution: I had a look and I could see that you're using a custom theme. Also, I could see that the categories are added using the category_badge function. However, in order to get the categories in English, a separate function called category_badge_en is available.
The only function used in index.php file is category_badge that only takes the Polish badges. You need to use the category_badge_en function in this file too in order to have the English badges.
This is the technical support forum for WPML - the multilingual WordPress plugin.