For starters, I'm aware I handled this badly.
Situation:
Christian writers group. We're accustomed to praying for one another's needs, and some of the things we discuss are pretty personal.
The Interaction:
Member: So, how was your Christmas?
Me: Horrible. I don't even want to talk about it, but please keep me in your prayers.
Member: Oh, wow. What happened?
Me: I really don't want to talk about it.
Member: You don't want to tell me?
Me: No, I'm not going to talk about it. My family is okay, but I really need prayers.
Further incident:
The others in the group, later on, were fine with praying for me for an undisclosed intention.
Thoughts:
Although it irritated me at the time, it's not that she's rude or anything. I think it's just that she's so used to me sharing stuff and so used to the American tendency to say, "I don't even want to talk about it! I hate my mother and I don't want to talk about it because she wouldn't let me go to that dance and she set my hair on fire and I just don't want to think about it any longer! Can you believe it? And then she said--"
I just wish I hadn't had to be forceful in telling her I didn't want to talk about it. I wish there were a "pray for me" button I could push and then select "undisclosed intention" from the drop-down menu.

Results:
They did say they would pray for me, which makes me feel better.