I think the question is, have you found out something about your T online that surprises you? Bothers you?
You needed connection and in our world today, where we can't live without the internet any more - it provides connection.
So please don't feel bad, you have done nothing wrong by googling your T, seekersinking.
But I do want to point out something, hun..
When you looked her up before and found confusing things on her facebook page, it troubled and conflicted you. I wonder how helpful it is for you to google her, or if you are hoping to find something that restores your faith in your T (or if you are trying to confirm your conflict?)
Have you brought up the last thing with her?
I just worry that you will be hurt and I like you so much, I am sad that you are having a tough time and that you feel you lack connection at the moment.
But just googling her is not ground for termination at all, please don't be afraid of that. The stories on here when people have been terminated because of online stuff usually have a lot more circumstances and big privacy invasions. You didn't do that, I am sure.

I'll pm you later, ok?

Love,
Amelia