Does prozac work?

I was diagnosed with social anxiety and depression. I am a 21 year old male and the last 2 years of my life have been hell. I self medicated for a long time and I quickly lost grasp of everything that was important to me. I became dependent on Alcohol and it eventually landed me in jail. Now I am on my way to recovery and I feel ok not drinking for days on end. I ve always turned to alcohol for social situations. My anxiety, I fwlt got worse and worse and I was drinking to alleviate anxiety for things such as going grocery shopping, going to the movies, or anytime I left the house to hang out with someone. My docotr got me on Prozac 20mg everyday for a month. I am currently on day 12 and i dont feel any different. Is it too early to say prozac wont work? However something interesting happened. Around day 5 or 6 I felt a feeling of complete comfort and happiness. I was doing well at work, I wasnt worried about how the world viewed me. I went to the mall and thats when it hit me, I have never felt the way I did that day. I felt confident, happy almost invincible. I am not sure if it was just a placebo affect because it lasted for like 3 days and then I felt normal again. I read somewhere that if it worls early this means it wont work at all. I have faith in these pills and I hope that there is still time for the drug to take its full effect. Please i dont need any negative feedback, i know the risks getting on this medication so i dont need a lecture.