Hi, Isit. I'm so sorry to hear about your DD. My DD was also prescribed fluoxetine, but it seemed to work for her.
I really do sympathise about the school and friendship issues. Perhaps you could read the thread about anyone having a DD that's been in a psychiatric unit in this section of the boards? I've written a couple of long posts on there and there have been a few other really helpful posts, too.
I also have experience of the wanting to get better and then saying that it's all too hard. DD was in a unit for three weeks recently and is still saying that she is kind of "planning" other stuff.
If you think about it, as the staff at the unit told me, it's taken a long time for your DD to get to this low place, so it's going to take ages for her to get to a well place. We cannot just expect things to happen quickly. My DD has an EIS (Early Intervention Service) counsellor who has just recently told me that DD will be having counselling from them for three years! I did not expect such a long timeframe.
It is hard, being and dealing with a DC who is so low. Talk to her and ask her how she wants to be treated. Does she still want the normal jokes, etc that you get with family life? My DD did. We usually discuss stuff at the dinner table, too.