Why don't you want her to bring up her period?
What made you think about this?
she knows I don't like talking about it and it bothers me a lot.
If you don't like to talk about her periods it's ok. Just tell her that politely.
I can't tell her that. It's not like we have a healthy relationship in the first place.
I'm sorry that you aren't having a great relationship with her, but you should at least be able to tell each other stuff that bothers you.