M.R.
First of all, congrats on your new baby! Mine just turned 9 weeks and she is absolutely amazing. She too is going through a rough case of baby acne as well. I would recommend some products by Aveeno. They have the lotion and the mild baby soap as well for bath time. I noticed the Johnson's products actually irritated her skin more, and ever since we switched her face is progressively clearing up. Hope it helps!
M. R