The blue under baby's eye is more in the inner corner of eye. It goes from the corner of eye over bridge of nose to other eye like one continuous blue band. This comes and goes. It is not just there when she has a stuffy nose, but also when there is no other symptoms.

Since your baby is only 2 months old, the best advice would be to bring this up to your pediatrician on the next well baby visit.

Yikes, just make sure that no one overlooked a possible heart problem. Look at the baby's fingernails, gums, and toenails for blue coloration.

Blue skin (cyanosis) is the first sign. There have been many moms discharged from the hospital where the doctors never picked up on a heart murmur.

Otherwise, that could just be blue because of the thinner skin in that area compared to the rest of the face... hopefully, that is all.