@Tomoswatts,
Self-harm is a mental health issue, not a crime. Someone in my extended family suffers from self-harm. In the US there is a lot of support for people who self-harm in the mental health community. I think from your writing you are in the UK... but I would be very surprised if it wasn't the same there.
You should talk to your mom and be open about it. And, you should get help from a therapist or counselor. You can start by talking to your doctor. Your nan didn't react very well (many times people don't know how to handle this even when they mean well). Tell your nan you want to get help from a therapist. She is probably trying to help you... but she is going about the wrong way. Guilt is not helpful for people who self-harm (as I am pretty sure you already know).
That being said, if you are under 18, it is reasonable for your Nan to not want you to be alone (for just a couple of weeks). In my experience, there is a time where a child and parents need to figure out how to deal with self-harming, there is a time to rebuild trust. A therapist will help both you and your parents.
Also, there is a lot of ignorance about mental health issues. Don't listen to people who don't understand what you are going through. There are also some harmful voices on the internet... I hope you stay away from them.
I hope you can get connected with healthy, supportive people who will help you.
From what I understand, guilt is a big part of what makes so difficult to deal with. Your mom will be OK, please take care of yourself... you are worth it.
And get yourself some help, a good therapist who can help you, and healthy people who can support you as a person while you deal with this.