>If you really love her though, be contented with what you know. Don't force her to spill out her past
This sums it all,...
She has actually started to open to you, since she told you stuff from her past. If you react badly to that, it's not very surprising that she will hesitate to tell more. Just show her that you are comfortable and non judgmental, and make clear that you will not force her to tell what she is not ready to tell.
I don't think you should feel insecure about all this. On the contrary, the fact that she speaks about sensitive things is a very good point for you, and you should take it as such.