I would wait until you see her next and then simply say something along the lines of 'How are you? I was worried something was going on because you were sounding different in your emails.'

I don't see anything wrong with apologizing for your reaction to her bad childhood story. I agree its not necessary, and I am an over apologizer, but I understand the sentiment. I had a similar thing happen with my therapist early on, and I wasn't happy with my reaction. I realized later it was because I was afraid of emotional closeness, which is what would have been required for me to really empathize in that moment, so instead I just withdrew into a silent stare. Around this time I decided I probably wouldn't be a great therapist myself and it was a good thing I kept my day job .