So sorry your girl is suffering - our children's pain is our pain isn't it - bit confused as you say "she can't get on with her mom who has her own issues" - assume that's you? It's not really surprising she doesn't want to talk about depression - I think this must be very hard for a young girl, as at that age they just want to be like everyone else don't they, are can be very self conscious which only makes things more difficult.
I'm sure you know that the simplest thing can seem an ordeal when you're depressed so it's not surprising she couldn't face an audition and gig tonight. Also it's not surprising she hates school, as it must be a real struggle to concentrate and try to act like nothing is wrong. I wonder if one of her relatives is bipolar, as there is as I'm sure you know a hereditary factor with this illness.
It isn't clear from your post whether you have a mental illness or not, but if you have experienced depression and anxiety you will know that it is a horrible illness that sucks the life out of you and makes you feel worthless and hopeless. I wonder why the GP didn't refer your DD to CAMHS as I'd have thought that would have been a first step. I also wonder if he mentioned the website YoungMinds which I think she'd find helpful.
Does she have any friends who are able to understand that she is not well at the present and can support her. It's difficult enough for adults to try to understand depression and I think it's not really possible unless you have first had experience, so must be more difficult for young people. Although having said that some youngsters (especially girls) are very emotionally mature these days.
I think the best thing you can do is to accept that she is depressed and not have any expectations of her just now, let her be, don't press her to discuss how she feels, but be there if and when she does want to talk. Try to encourage her out of her room (if she's spending a lot of time in there) as depression makes us want to isolate ourselves and that's not always a good thing, though sometimes it's less painful to not have to be with others. You might find there are certain times of the day when she's better than others - sometimes depression gets better in the evening with the mornings being the worst times.
IF you don't know very much about depression (and I'm sorry if you do...) you might find the MIND and RE-THINK websites useful and YOUNGMINDS.