I would suggest you try AA, it can help with your drinking and may also help with your social anxiety. You don't have to talk if you don't want to. But eventually you should, and it will be great practice to overcome your anxiety about talking in front of groups. You get to decide what you are going to say and how long you will talk. Start small, just say just a couple of sentences, go for 20 seconds. People in AA will be very supportive.