I use aveeno bath and lotion, my daughter had/have eczema bad.

its completely normal for a baby to get acne, buy some eczema baby cream it will work wonders and just make sure to wipe face after feedings good

id have it checked by a doctor and see what they say. i wouldnt be so open to over the counter things unless a doctor says its safe for the baby and the baby wont have any reactions to it