It sounds just like eczema actually.
You can try applying OTC cortisone cream (make sure it's in a LOW enough dose to be applied to facial skin).
There's also a prescription called Elidel which is a NSAID suitable for all skin types and locations, including safe for use on children, and safe for use on the face, available by Rx.
If it's an infection, you may want to try some bacitracin or neosporin, very, very lightly applied 2-3 x day, and you should notice a difference within 48 hours if that's what it is.
I can't dx it, obviously, but at least those ideas all pertain to the same thing which is that it might be a type of dermatitis and the ways to treat it are similar, and those are usually pretty safe things to try.
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