The intro/extroversion as well as the age difference plays a huge part in this, I think. She is young, and as much as she may love you, she wants to go out and be with people and socialize. And because many young women are very insecure in who they are and their sexuality, they enjoy the attention from other men as a form of validation - even if it honestly means nothing else. That is probably why she was worried about the smile on Facebook. It's nothing you can help, even if you shower her with love and attention, her sense of security can only come from within herself, and that will just take time. She has some growing up to do.

I think the most important thing for you to do is not to be vengeful about it. Whether in this situation or in the future, revenge will only poison the relationship and make it harder to recover whenever there is a problem.
If you really feel like she is trying to make you a sugar daddy, then it might be time for the relationship to end. But, if you think it's more a matter of maturity and communication, you should be able to work things out. She needs to be open to understanding your introverted lifestyle, and you need to accept that she is young and still blundering through her youth.

If you love each other, all you need is a little understanding and acceptance, and you'll be just fine :)