If the CBT does not significantly improve her mood and make her seem more stable then I think that she could do with a more in depth assessment from a community psychiatric nurse (CPN) or a psychiatrist. So I would keep an eye and maybe she could push her doctor for this? Maybe she would let you go with her to the appointment?

CBT can be great for depression. Sometimes it is all a person needs to kick start a recovery. However, there are elements of your story that make me think that this may not be the case for your girlfriend. Particularly aspects of it that exactly mirror my own experiences. So I'm not qualified to be saying anything. But please just keep an eye. The idea of seeing someone like a psychiatrist can be scary, but in my case I did not want to go, but now I did I am off the meds completely, getting therapy and doing a lot better as a result. So sometimes the system surprises you in a good way. I self harmed while I was at uni over ten years ago. I'm only just now getting the help I need. I think it is great you care for her so much and are asking for advice this way. I hope the CBT will help, but it is not the only option if it doesn't. Also, Sertraline may not be the right antidepressant for her, but it could be, and six weeks is not really long enough to tell. But I'm glad they are putting her on a lower dose, anything above 50mg used to make me into another person. But I know it doesn't have this effect on everyone either.