why do you drink? I wouldn't recommend drinking as appropriate strategy in dealing with social anxiety, I am dead serious about this. you can fuck up your entire life by making anxiety even worse, or worst case, you become a bloody alcoholic. this of course takes many years, it can last more than 10 years until you notice that you are an alcoholic.
anyways .. if you get a terrible hangover after drinking on Effexor thats because you are drinking way too much on Effexor. maybe you shouldn't drink at all? I know, nobody likes this perspective.
As I got Zoloft I began to overdose the pills to kind of cure my hangovers away (they were quite terrible too), once I did a big mistake, I had overdosed the pills (don't do that) and killed one ore more bottles of whiskey with a friend, than I managed to get thrown out of a bar where I touched some girls private parts while all the others (boyfriends etc.) were around. Then I got into a different bar, startet a chat with a random girl and asked about 100 times after her name... so kids, don't try this at home and don't ever take too much or use drugs, and most important: don't do alcohol!