Girl threatening me about my baby?

I got pregnant by my ex during a one night stand. We've been somewhat seeing each other but there's a few things holding me back from getting into a relationship with him, including this: he has this friend who is a girl. I've had issues with her in the past because she was flirting with another ex boyfriend years ago and I told her off. Since then she talks crap about me, 24/7, even to my baby's father and I've just ignored it. She supposedly is pregnant now claiming she's 2 days ahead of me (I'm 8 weeks today) but says she conceived on the 6th of September. So she'd actually be 10 weeks. But she's been guilt tripping my baby's father about how hard it'll be to be a single mother. She called him, and he told me how she was super excited that they have the same birthday month and now their kids would too. She then posted a status 2 minutes later on Facebook about how she was SO excited for June because her and her friends babies would be due at the same time, probably "within days of each other", and dropped hints about who the friend was, telling everyone he and her share a birthday month. We haven't announced it yet. Some of my family doesn't even know. My brother put two and two together based on her "hints", although he already knew I was pregnant, I hadn't yet told him when my due date was, and he found out from there. My S/O said he'd speak to her and never did, so I had enough. I figure if she's telling strangers and dropping hints, she's for sure telling people she knows, with our names, and it's a small town. So I politely told her to delete the status and it wasn't her business to tell people. She went OFF. She started calling me crazy, saying my pregnancy hormones are insane, that it "wasn't even about us" it was about her other friend who is pregnant and happens to have the same birthday month as her and is due in June 🙄, started calling me "little girl" when she's a year younger than me and about an inch taller, calling me a bitch, stupid, a waste, etc, then went into my baby's father's inbox and told him I was crazy, blah blah. I was super respectful the entire time. But this is the kicker: I told her she wouldn't be allowed near my baby (not just based off this, she's been in juvi as a teenager, smokes, does drugs, drinks 24/7, uses completely foul language, etc and she had the neve to tell me that she would be allowed because it's my baby's fathers kid too. I told her we'd already agreed she wasn't. She then said she'd just go to his house and see the baby. I told her I have my own apartment and the baby wouldn't be living with him, if anything, he's moving in with me. She then said duh I'm not stupid (lol) the baby will go see the grandmother (his mom) at some point and then you can't stop me. She kept going, saying the future is the future, I can't do shit about it, that they're best friends and he'll let her, etc etc.I simply said goodbye, that's it, and she  then said she had something that my baby's father said that would "really piss me off but it's between her and him". I have his Facebook password and he doesn't have a cell phone and she's not exactly attractive, so I know she's just trying to start crap, but honestly lmao.