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I don't think so. A few sites I checked out don't mention any side effects. It is considered a "pregnancy hormone" so the baby would have been exposed to it in the uterus before birth through the placenta. Hope this helps.

No, the baby will be fine. It's no more harmful than many store brand lotions which actually have estrogen in them. If the person puts progesterone cream on their arms, it's going to be mostly absorbed into their own skin before any of it might transfer-rub onto a baby.