Is it normal for baby girls to develop lumps of tissue under their nipples like breasts?

Yes. A burst of your hormones pass to your baby shortly before delivery, one of the finishing touches in preparing her lungs to breathe air when she is born. These hormones include estrogen and androgens, and can have several transient side effects. Real, mature breast tissue forms, creating firm lumps under the nipples. Some babies even leak some real milk from their breasts.