It's definitely possible that your friend is waiting for you to talk to her first. I think people often don't understand that it takes a lot of courage to say "I'm struggling with this" and are waiting for the other person to ask! If you want to talk to her again, I hope you can try to bring it up with her. Would sending a message feel easier than trying to bring it up in person?
It's really thoughtful of you to not want to upset your family by telling them, but don't forget that you have just as much right to consideration as they have. I know it would be a big decision to tell your family, but it could be worth considering, especially if they might be able to help with the costs of therapy.
Has RAINN been helpful?