You've said it perfectly yourself, try not to get too emotionally involved. Others have explained more eloquently than me in this thread but you really aren't at any sort of mature level in the relationship, it's in the infancy stage, it really isn't a thing yet even though you think it is. It isn't any more or less real than the conversation you and I are having now. Again, as others have pointed out, it can feel very real but that's a potential trap (I've been there, met someone via YouTube way back in the day, had a tonne of chemistry, talked for a year and met up, and it wasn't the same (I know you guys have met up and you still feel a connection)).
If it's eating away at you then I'd advise talking to her about the FB post, but only if you can't put it out of your mind.
But then once again you're playing directly into her hands if you confront her about it, I'm not suggesting that she's that way inclined but that post might speak volumes, we communicate a lot on social media and for many it's a way of prompting a reaction. Who knows, perhaps that post was intended to get a reaction from you? I really couldn't say. Also, she's allowed to post what she wants. How did it end with the father? Perhaps she still has feelings? If the father turns around and says he wants another shot at the relationship do you really think you're going to get a look in? You've got to put yourself as your priority, whatever it is that you're seeking. Anything else is setting yourself up for hurt.
Similarly with regards to confidence, it's not something you have or don't have in my opinion, it's a blade to be honed. If you're on dating apps, why not start up conversations with others you may have matched with? Even if there's zero intention of going anywhere, it might build confidence for you.
Ultimately you don't have to do anything right now if you don't want to, you're in a potentially strong position, but the way you're acting and potentially behaving will suggest to her that you're utterly besotted and not going anywhere else for attention/connection. And if it's one thing women hate, it's an easy catch at the start of a relationship, and if the chasing is unbalanced it rarely ends well.