Cold sore or baby acne??

So I woke up this morning with a cold sore on my lip. I immediately took medication for it. My little one just woke up from an hour nap and now has this under his eye. He’s only a month old and this is red around it unlike his other little acne/milia spots. I have been very cautious and continually wash my hands. I’m waiting for a call back from the doctor but has anyone seen something like this or has experience and can say it doesn’t look like a cold sore.