I can't help from the perspective of a parent, but I became depressed myself at that age, so maybe I can offer something from that angle. I didn't drop out of college, but my attendance was absolutely atrocious, I wasn't really doing any of the work I was supposed to be, and I was also bulimic. I spoke to a teacher at college, who was really supportive, and she persuaded me to go and see my GP, who gave me anti depressants and referred me to the CMHT. However, although I got help for myself, at no point did I tell my mum what was going on - she knew nothing about any of it. I assume she had noticed my low mood etc, but she didn't know about my eating disorder or depression, she didn't know I was on anti depressants etc etc. It was quite a few months before I told her anything. So your daughter may actually know that there is a problem, but not want to talk about it, or want anyone to know about it. Mental health problems can make you very secretive, or it did me, and even now when my mood crashes my instinct is to keep it to myself and try and hide it from everyone around me.
I would say that at this stage forcing her into a clinic would be unlikely and unhelpful. It's very unusual to be hospitalised for mental health problems unless you are very at risk, so acutely suicidal etc. I'm not saying it won't happen at some point, it could if she continued to be unwell, but right now it is a bit like running before you can walk - she hasn't even spoken to anyone about what is going on. What you can do is go and see her GP and talk to them about your concerns, and if she is still refusing to see them herself then I guess you can try and insist (but I don't know if that would work or not? Probably depends on the type of relationship you have) or the GP could possibly do a home visit, or call her in for some type of check up and try to talk to her then. They can then refer her on to other services as required. The other thing you could do is book her some sessions with a counsellor, but if she is insisting there is no problem then she would probably be unlikely to go along with that, so I would go the GP route first.
It is really hard to know what to do, particularly if she won't speak to you about it. Don't push her too much - if you continually nag her about what is going on for her then she may well close up even more, but at the same time do let her know that you are concerned and want to help, and are there for her to talk to if she ever wants to, and also tell her that if she wants to talk to someone but not you that you could arrange for her to see a counsellor instead and that it would be totally confidential etc etc. Try not to take it personally that she won't talk to you - there are lots of potential reasons why she may not want to; I know that for me a big factor is that I didn't want to worry people, and I knew that they would have if they knew how I was feeling, so I just kept quiet. It wouldn't matter how many times people said that not talking would worry people more, that just didn't make sense to me. Depression can screw with your thought patterns pretty badly, and things that seem obvious to other people can just make no sense at all when you're not well.
I'm sorry I can't help more - to an extent you are limited by her refusal to admit there is a problem, but she may be more willing to speak to someone else about it, or there are sneak tactics like getting the GP to get her in for something else if it comes down to it, or even a home visit. In the meantime just offer her support but don't smother her as it could just push her away. I really hope you manage to get her to agree to some help.