All of the things you are doing sound like the right thing, and it sounds like she's also accepted that she has a problem and wants to solve it too, which is really important. Here's some things from my experience which may help.

Just being there, even if you are not able to get her to talk or she doesn't want to touch you, just being there is helping.

When she is communicating, just let her talk and talk. Your not supposed to have all the answers. You are not her therapist. You can listen, even if it's just a way to talk herself to sleep it helps.

Try to remain calm. I know it's really hard to be calm when you are watching someone you love fall apart. But, if your voice is calm and you tell her you believe that she can get through this, she is less likely to feel like she is damaging you and this may be part of the reason she pushes you away.

Try to focus on the everyday things. Depression can feel very dramatic and out of control. Simple, everyday things can be very reassuring. A simple task like doing the washing or tidying the room can give a sense of achievement to someone who is depressed.

Finally, look after yourself. The last thing you need is to suffer from anxiety yourself, this will not help either of you. Even professional counsellors go to counsellors. There are phone lines and other forms of help, use them, not just for her, but for yourself too. This is a lot for anyone to deal with and it is not selfish to think about how this is effecting you. Has she also tried using some phone lines or other emergency help? It might bridge the gap while you are waiting for the therapist.

I'm thinking of you both, hang in there.