4 month old with Dennie Morgan folds

My 4 month old son has eczema and the last few weeks has developed multiple lines under his eyes. I have read on doctor google (yes I know that's dodgy) they are allergy related and are called Dennie Morgan lines which if the allergy is not treated the lines may become permanent. I'm saddened to think he may go through his childhood with these lines. His pediatrician wasn't concerned about them and said that is just how he looks. They just do not look normal. What I would like to know is has anyone else's child had these "allergic lines" and did they go away.