I wonder why your new friend asked you a specific private question about your family. Were you talking about your family with this person already? Or did they ask you this question out of context?

Did you tell her that her question made you feel awkward? I've done that with people, who've asked me questions I felt were none of their business. If I don't want to answer, I just tell them, "I don't feel comfortable talking about that."

Does she know that you are a very private person who doesn't like to talk about your personal life? I would mention that to her. There's nothing wrong with setting up boundaries early on with new friends. It helps them understand what your lines are; what not to cross, what's ok. It's perfectly acceptable to casually mention, "You know, I'm a private person. I don't really like to discuss my family with people." You don't even have to apologize to them for it. It's your life, after all.

I've struggled with codependency my entire life, so I can relate. I used to be much more of a doormat until a few years ago when I realized that if I don't set my boundaries, people will walk all over me and think it's ok unless I tell them what is and isn't ok with me. Just think of it this way: people will only go as far as you let them...most of the time. You have to draw the line for them sometimes or they won't know how far they can go.