Your 2 year old does not have eczema but she has a skin condition found in babies and young children called seborrhoea. This is not due to an allergy. The condition will clear up by itself. Do not use a strong shampoo on her scalp. wash her hair with Elizabeth Anne baby shampoo two or 3 times a week. Apply Mylocort ointment very lightly to her scalp once ady until her scalp is better.
I am not sure about your baby's mark between her eyes as you do not mention if it is raised or flat. It may be a strawberry mark which will fade away by itself with time. No treatment of any kind is needed.
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