It can definitely be difficult to feel safe discussing things of this nature. If you think it might be easier or help explain symptoms you're experiencing, maybe you could say something along the lines of 'I went through some difficult experiences both as a child and as an adult, but I'm not currently ready to talk about them. I'd like to build up some safety in our therapeutic relationship first.' just to kind of give her a heads up that there is a history there AND make it clear that you're not ready just yet to delve into something so difficult.
I started with a new therapist back in September and we've still not really gotten into the vast, vast majority of my experiences because it takes time to build up the safety in the relationship and build up skills to be able to tolerate discussing them. There's nothing to say you need to delve into the worst stuff right away, and there's absolutely no shame in taking your time to build up skills and safety in your therapeutic relationship before throwing yourself into the deep end.