After recovery, you still have the TB antibodies in your body, which means you are a carrier. If you ever have to have a skin test, such as the Mantoux, it will turn up positive and you will then need a chest x-ray. If you have active TB, 3 positive sputum tests and a positive chest x-ray is conclusive. Antibiotics are started and the treatment lasts for months. So in answer to your question, no there is no immunity. You are just as likely to catch it again as anyone else.