That’s a hard one, Jessica. And that’s really an extreme reaction. By “vomit” I am assuming you mean the production of a lot of throw-up, not merely a bit of liquid drooling out the corner of her mouth. She’s undoubtedly teething now, and babies produce a lot of saliva (and some have a lot of discomfort) during that time. That may be part of the problem. Let’s take the car seat first. I would guess that there is something about riding in a car that makes her anxious. Observe carefully and see if there is a pattern (she throws up on the way to child care, she has on some particular garment that is uncomfortable, etc.). Seeing other children ride happily in one might help. Perhaps you and a friend with a child of similar age could go somewhere in the car together. Being with another child who handles the situation calmly may help reduce her anxiety and resistance.
Throwing up in the bed is more serious. You definitely don’t want to leave her in the crib with vomit in it. Babies can aspirate vomit, blocking the airway, and actually die from it. If she wakes up and cries, try picking her up and holding her for a few minutes and see if this will prevent the throwing up. Then give her something special when she goes back in her crib—a cuddly toy, a pacifier. I am a firm believer in the magic of pacifiers, incidentally: they provide comfort and reassurance and don’t do anything to get the incoming teeth out of line. If she is still doing this at the time of her next check-up, be sure to talk to your pediatrician about it.
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