Here's another one
You definitely haven't done anything wrong! There's no need to feel bad - sounds like she just got moved by your story, excess of empathy maybe - or possibly it pushed some of her buttons, who knows. You really didn't say anything wrong!
This is not your fault, at all, don't let your head tell you that there's something you should be beating yourself up for. Sometimes I've found that once you start dealing with stuff, your head fights back even harder as it's way of thinking starts being challenged. Mine certainly does that, I had a huge battle with myself earlier this week!
Counsellors and the like usually have their own support network and therapy sessions to help them cope with the job, she will have some sort of support - or at least she should, if they're any good.
Maybe have a conversation about it with her, tell her how you're feeling about it and figure out together if she is in a position to provide the help you need? If you feel that she's not the right person for you, then you can always move on.