There is nothing for you to apologize for. It was a professional mistake on her part to self-disclose about her childhood experiences, and, frankly, it's not professional to make personal disclosures a regular thing. I don't necessarily have a problem with the regular exchange of information such as articles, upcoming events, as well as for her to check how you are doing, but the regular disclosure of personal information is unprofessional. And if her way of communicating changed because you didn't react to her childhood disclosure the way she hoped you would, that's a good reason to run away from her IMHO. Of course, we don't know if that's the reason, but if it is, then she is not fit for doing therapy work and the sooner you find a new therapist the better.

It's not your role as a client to give your therapist emotional support, and if that's what the therapist seems to be seeking, the best thing to do is to quit seeing her. Otherwise, you may see the role reverse, in which you'll be the one doing therapy to her while still paying her.