I think this is good advice from MissVerinder.
It is a dreadful thing to have happened, but as her mum you are not necessarily in the best position to offer all the support she needs. It sounds like she needs professional counselling to get over her trauma and learn to live with the aftermath. You are not a professional counsellor, besides I am not sure close family are ever in a position to deal with this sort of thing.
I have a 14yo dd who is suffering from a chronic painful joint condition combined with depression and anxiety, and I have come to realise that I do actually need to back off a bit; running myself into the ground won't help her either. She is getting professional counselling and I am also making a deliberate effort to back off a bit, involving myself in my own work (academic writing) and letting others give her part of what she needs. And yes, she also uses the "You are my mum, you have to be able to sort everything"- line. It's hard, but I find if I can do it firmly and pleasantly it is possible to say "well, as your mum, I am now telling you to talk to the school counsellor/Dr X/ etc" and she will kind of accept that.
You may also want counselling (if you are at uni, they should have the facilities)- I found it helped me to have a space where I could talk about how things affected me.
I would make very firm plans about exactly how and when you will support her during the op (I will come to the hospital for X appointment on day Z) and the rest of the time I would try to get away somewhere where I could wholly concentrate on that PhD. You need to do that thesis- for her sake as much as for your own.
And tell her very firmly that she must have professional counselling to get over this, that you cannot do the same thing for her as a doctor could.
Am just about to leave the house- leaving dd in bed- to start proof-reading my book. I am doing it for both of us: dd needs to see that you can get on with life.
Fingers crossed for all of us!