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Eczema per say may not lead to hair fall...but it can be a indirect effect in the form of stress. As the baby is only 18 months old ,we should not worry too much ,but yes you have to rule out nutritional deficiency
as well.One should check for serum iron
level,serum zinc level etc.At this young age even protein deficiency can cause hair loss and thinning of hair. So, kindly consult a dermatologist
who can help you with the proper diagnosis and treatment.