C.C.
My daughter did the exact same thing. I am also a stay at home mom and since she was my second, I didn't leave the house much and unfortunately she was not socialized with other people. She still has a little anxiety, but not as bad. Socialize her as much as you can, with other people holding her and with you out of the room. I joined a playgroup and just being out of the house and seeing other people has helped. When we had to get out and have a sitter, she would usually scream and scream and the only relief was placing her in her carseat and rocking her to sleep. It was something familiar to her and she felt most comfortable in there, rather than in someone else's arms.