Just be really calm and gentle. A cat trusts you most if you are predictable and non-threatening. To a cat, sitting quietly in the same room is a sign of being friendly and polite. Cats are solitary hunters by nature--unlike humans and dogs, socializing is not a basic need for them, but rather something they do by choice because it's fun and they like the other person or animal. So, she will want to make sure she's safe and secure before she starts up with socializing.
She's neither broken nor traumatized, just shy. She may come out of her shell, or she may simply become a one-person cat who's most comfortable with you but darts under the bed when company comes. I think sometimes people are too worried about shy cats because they unconsciously think of cats as a sort of small, furry human, and they know that they themselves would hate to be alone and not be able to reach out to others yet. But of course they aren't humans; they're cats, and for a cat, socializing is something they do in their "spare time", once their other needs have been met. Not that they don't like to socialize--they do; and during kittenhood, before about twelve weeks, they need it. They just aren't wired up as social animals the way we are.
As for petting her, she seems to feel a little threatened by it right now--physical contact from a big human probably overwhelms her somewhat. Many cats will let you pet them in one place but not another; like, maybe she'd let you rub her head before she let you touch the rest of her (or vice versa; my cat Christy hates having her head touched because she had to have ear drops and hated them, so she only lets you rub her head when she is very calm).
It's always easiest to approach the cat from the front, so she can see what you're doing and that you don't mean any harm. Let her initiate at least part of it--for example, stretch out your hand, let her sniff your fingers, then stroke along her cheek. If she pushes back against you, you know she'd like to be petted. If you let a cat initiate the cuddling, it's much easier to figure out whether she wants to cuddle. If she ignores you or draws back, she's probably feeling too nervous to enjoy it at that moment, or just wants to sit quietly rather than interacting right now.
Play often entices a shy cat. Try a wand toy or a dangled string, something that doesn't require you to get your hands too close. Bring her treats (whatever food she happens to like, especially things like goat milk or wet kitten food--she's still a kitten; it's practically impossible to overfeed a growing kitten). Let her associate your presence with fun and food. And spend a lot of time just in the same room, mostly ignoring her, just going about your usual business, so that she gets to know your patterns.
BTW, if it makes you feel any better, Tiny was nine months old and semiferal when I first adopted him. He had been living on the streets--I think he must have been dumped as a kitten. I thought he was feral at first, but he warmed up so quickly--within less than six months he was acting like a shy house cat--that I knew he must've had a human owner at some point. Today, at age three, he's an affectionate one-person cat who rubs around my legs, headbutts me, occasionally jumps into my lap, and climbs into bed to wake me up when the clock radio goes off in the morning.