Her immediate reaction was, She's having sex. She has chlamydia of the throat? That's not normal flora for there, she had oral sex.

This is not meant as medical advice, but...

My personal approach would be to be straightforward. Something like:
Let me level with you. I'm not 5. I don't believe in Santa. I don't believe in the tooth fairy. And I don't believe in miracles.

You were engaged in sexual activity. Perhaps not vaginal sex, but you got intimate with someone's private parts. If you try to tell me otherwise, I'll know that you lie. Stupidly.

Now I'm not going to go tattling to your mom. And I'm not going to ask details. But I'm going to tell you straight out that you were lucky - you have something that is easily cured. Maybe you won't ever be able to have kids. If you get it treated promptly, you'll improve your odds there. But it could just have easily been something that would kill you.

I like you. I want to see you live. And I want to have an in depth conversation about how to keep you alive when you are willing to listen.

Then bug her every day or 3 about when she's going to have that conversation that she needs.

An incidental fact. A lot of kids think that the medications that we have for AIDS is a cure. They're wrong. At great expense and with many side-effects, you're kept alive for quite a while. But even with everything that we have, you'll die in the end. And nothing that I know of promises that there will ever be a cure.

Good luck,
Ben