err what? I think you need to hear an outside perspective here. An ex likes a photo and new girl immediately brings it up? knows who she is? and implies it's hassle. Yet, you see her post a photo of her ex on FB referring to her kids and his looks years after he's supposedly out of the picture, and YOU don't discuss that? I'm not suggesting you're stupid, but, don't you think that's ridiculous? Do your thoughts and feelings not matter? If you want this to be something it has to work both ways, you can't ignore your own red flags, it can lead to all sorts of problems including resentment.
Gee lucky you. Better be on your best behaviour. Look it sounds a bit mean but I'd suggest you slow things down. Making plans for some event 6 months down the line after a meeting in a car park and some other event isn't sensible, you don't know each other very well.
You had no problem talking to your ex about the like but can't do the same with the new girl, it sounds like your ex was honest with you with what she did and no harm was done, but you've turned it into a big deal.