It’s really weird that she called you crying over a Facebook picture with an ex-girlfriend at 5:30 a.m. You can see the date the photo was uploaded on FB, so IMO she should’ve been able to tell it was old. If was a recently uploaded photo by an ex, I can see asking about it (I once learned I was being cheated on thanks to FB), but not in this way.
You weren’t together when she went on vacation and it sounds like you were never exclusive notwithstanding, so she was/is allowed to flirt with any and all impressive men she meets on vacation or elsewhere.
Honestly, this is a lot of drama for three months of dating. I’m scared to ask how old you are. A FWB with this woman likely won’t work either. I think you should both move on. If you’re looking for a relationship, you’ll want calm and stable.