Without seeing the spots to evaluate, it would be hard to say for sure, but milia and baby acne (two types of skin lesions) are fairly common in the newborn and usually clear up on their own without any treatment. You can find pictures on Mayoclinic or other sites if you search online. The best thing to do if you are concerned is talking the baby's doctor about it.
Ask the pediatrician just to be sure, but it's probably baby acne. My daughter has it on her cheeks and the back of her neck. Our pediatrician said its leftover hormones from when she was in utero. I've just been wiping her face with a warm wash cloth and that helps somewhat. I'm breastfeeding and my hormones are still wacky, it shouldn't last past 3 months.
Re: Red bumps?