Enochi, you are doing a great job! I have been on both sides of this, and I know it can feel very 'unrewarding' and helpless to be in the situation you are in, not to mention exhausting. I would also say that even if she can't talk about it, I am sure your girlfriend sees and appreciates your support.
Given you have experienced anxiety and depression yourself, you will have some personal knowledge as to how they can affect a person which is a good start, but if you know some bits and pieces about her history, something you may be able to do is try and learn a bit more about those kinds of traumas and how they can affect a person. By that I don't mean asking her directly, as she will likely close up even more, but there may be some hints from what she has said that may be able to look into, ie. physical/mental abuse or whatever the case may be.
In terms of therapy, it can possibly help, but as you would know, it's a matter of finding the right person at the right time and in the right timeframe, so it's important to look at that as a long term goal. As others have said, I don't think she should be worried about costs as there are subsidies available, but I feel it is important for her to be able to consider it as a viable option for her if it is to have any chance of working. How to do that, though, I'm not sure! As you have had some success with therapy yourself, perhaps you could try relating some of your experiences to show her how it helped you? Therapy can also be a bit of a 'mystery' sometimes. It may be she doesn't even understand how it works or what it might be able to do for her, and just has an aversion to the word 'therapy'. It is worth noting that there can be a definite lack of transparency in terms of what to expect before going to a therapy session too, which can make it challenging. Perhaps you could also do a little research into some sort of 'Therapy 101' to give her a good grasp as to what it actually is? It may not be what she thinks.
I hope this is of some small help to you - the others to have posted before me have also made some great suggestions. Good luck, and let us know how you get on!