SSRI's tend to have that sleepy side effect, except for Celexa, Lexapro, Zoloft (sometimes), and Effexor XR. With Effexor XR being the SSRI least likely to make you drowsy. I'm currently on it and it doesn't make me drowsy in the least and it helps a great deal. Paxil helped a great deal, but also made me drowsy a great deal. Celexa didn't make me drowsy so I would assume Lexapro wouldn't either. Haven't tried Zoloft.
'Social Phobia' though. None of the drugs really help with it. They have a very slight effect on generalized anxiety, _I guess_. But it's so hard to tell. The only thing that works for my anxiety is benzo's and even without therapy I have gained enough confidence while being on a benzo that I have gone from not being able to talk to strangers to being able to carry on a full conversation with anyone and not have a panic attack or sweaty hands or any sign of anxiety, just mild discomfort. Benzo's used in conjuction with cognitive behavior therapy is the way to go if you have a psychologist that is versed in anxiety disorders and knows how to go about it. There is a workbook that a lot of people use and I believe most people go through the same one while on cognitive therapy. Fairly good success rate if they use benzo's, not that great of a success rate if they don't have any benzo's to give them that boost of confidence.
Sorry for the big aside, however. They should just approve the whole class of drugs for 'Social Phobia' (is that even in the DSM-IV-TR?), since most of them are now. (sarcastic)