Can You Make A Kid Become Autistic?

Seriously, this is something I worry about sometimes. I know I can't literally give Pufferfish an autism spectrum disorder...unless you believe in the old refrigerator mother theories! But consider this scene...
Pufferfish and I are on a playdate at an acquaintance's home, with  three other adults and three other two-year-olds (two boys and a girl, all who are turning three this summer, just like Pufferfish!) Pufferfish has met them all a bunch of times, at different group outings, but she's rarely tried to play with them. I assumed she was just shy or overwhelmed because of the large groups, and thought that a smaller playdate, with just a few other kids, would go better. But while the other kids run and play together, squabbling over toys and squeezing into a cardboard box house together, Pufferfish won't leave my side or look at the other kids. If anything, she focuses on me, trying to get me to play with her or to watch her play.
"Why don't you play with Bella? Bella, are you going to have a birthday soon? So is Pufferfish! Look, Bella is wearing Dora shoes, and you have Dora on your jacket," I say, using tricks I learned while working in day cares to try to get preschoolers to bond with eachother. "Jonah and Elijah are playing tag! Try to get them!"
Pufferfish won't go. She clings to my legs and shakes her head.
"Go play, Pufferfish! Look at all of the toys! The other mamas are sitting down and talking while the kids play," I plead with her. "Nini will go sit with the grown ups, and you can play with the kids!"
She rocks back and forth nervously, and my heart sinks. Thats something I do, one of my Aspie traits. When I am nervous, tired, upset, bored, or whatever, I rock. Its a stimming behavior. I know Pufferfish has seen me do it many times.
I've also seen her flap her hands nervously, another one of my stims.
I am socially awkward and always have been. I care deeply about people in general, and I like being around people, but I have a horrible time connecting with others. When Little Bear was a preschooler, I joined a play group so she would have the chance to socialize with kids her own age, since she wasn't actually in preschool. (We couldn't afford it at the time.) Now that Pufferfish is almost three, I'm doing the same thing, taking her on outings with other kids, hoping she'll make connections. I try hard to "pass for normal" at these outings, something I bet a lot of people with invisible disabilities understand. I concentrate hard on not rocking or flapping or blinking frantically, not interrupting, putting an interested expression on my face and participating in the conversations about breastfeeding and organic foods and molding toddlers into college material. (These are the types of things people talk about in playgroups, by the way!) But I have a feeling the other adults still think I'm a little odd, by the way they exchange glances sometimes or frown at me in confusion. I often find myself scolding myself under my breath, "Shut up! Just don't talk! Don't talk, don't talk, don't talk!"
Of all of the kids in the family, Pufferfish is the one who has spent the largest portion of her life being one on one with me. When she was tiny she was often alone with me because she just needed more supervision than the others, and as she got older she was alone with me while the others are at school.
Its a big responsibility, raising someone else's kid. I know I give her a lot of pieces of myself. I love to read and do crafts. I have read to her since she was an infant, and before she was old enough to sit upright in her highchair alone I was putting paint on her fingers and teaching her to fingerpaint! And now she loves arts and crafts and she loves to read. I adore the dogs, and have always encouraged her to be gentle and sweet with them, and she has always been gentle to them, not scooping them up and dragging them around against their will like Monkeyboy, Little Bear and Tigerlily always did when they were little (and sometimes still do!) Pufferfish pets them, cuddles with them, throws their toys for them, and gives them treats like I've taught her to do.
But  I worry that I am also inadvertently teaching her the wrong things. I rock and flap when I am nervous, and she is starting to do those things. I am anxious around people, and now so is she. If she grows up to be a social outcast, it is my fault!
Is it possible? Can an adult caregiver who is an aspie pass it along to the child in her care? Or is Pufferfish just shy? And how can a socially awkward adult help a shy child get over that? What are your thoughts?