That was a huge thing to share your self harm here and to let us know how you are feeling. I am so sorry that things are hard to manage for you right now. Please keep some support numbers written down, perhaps even in your pocket, in the event that you need to reach for one quickly and you have it available and are not confused by searching for one. If you are in danger please call 000.
I also wanted to say to you that there is no shame in sharing what you are doing to yourself. It is a coping mechanism that people turn to when there seems few options. While it is dangerous and it is not encouraged it is real and there is no denying that people are using this way to feel, or to cope, or to escape..whatever the reason be.
I think it is very important for you to share this information with your doctor, as you mentioned she is very lovely and quite approachable. If speaking the words worries you, or blurting it out, you can write it down and say that you are having trouble saying these words but you need her to know. She will understand the sensitivity and start a conversation with you, start the words and you can then even respond with written ones if that helps too. As far as your question "what will she do?", she will probably react with calm, she may ask you some questions about how you are feeling when you do this, or if you are feeling anything at all, she may ask you what you are doing, she may not. I think all in all though she will be caring and want to provide you some time to share, if that is what you want.
I also wanted to share with you a thread that is here with people sharing how they cope and what they do instead of hurting themselves, some things here might help, they may not, I hope that you can have a look and consider some of the alternatives for you.
I also wanted to say how great it is that you have already written things down for your psychologist appointment, that you are thinking of what you want to share and focus your sessions on, to get the best out of your time and also to ensure you don't miss anything, I think that is great. It will also give you some sense of calm I think too, that you can prepare for the session and feel like you are managing it.
I am not sure if this has been helpful to you today but I wanted to say how proud I am of you for sharing.