My one month old has several small red bumps around her eyes what could it be?

Milia..: Milia are common, benign, small bumps that can be around the eyes and usually appear in the first 4-5 days of life in newborns. Around 40% of infants develop milia. Miliaria is a common problem of the sweat glands that occurs in 1.6%-4.5% of newborns. Both of these generally go away on there own. Make sure to ask your pediatrician, he or she will be able to tell for sure.