My baby has puss-filled spots on her back and face, they come up overnight and have no idea what causes them?

Impetigo: This is likely to be a bacterial skin infection. Please see your doctor who can take swabs from these spots and send them to the lab for analysis. If necessary, he may prescribe antibiotics as well.

Pus filled spots: some times milia ( heat rash) looks like pus filled spots. if concerns please get it checked out by the doctor as the alternative could be a impetigo( bacterial infection), which many need antibiotics.

Would need a picture: Hard to say. Would need to know age of baby and what they look like. It would be good to have a doctor take a look at the pictures of the rash. It might be a mild allergic reaction or a systemic illness.

Pos filled spots: These could be due to bacterial infection or chicken pox . Please consult your doctor.