hey there, my baby has (a light version of) eczema, too. i used coppertone's 'water babies' sunscreen lotion, 50spf, and she was alright. which one did you use?
the one i used, however, has lots of ingredients, so depending on how severe your bub's eczema is, you might want to consider to apply smthg else..
sorry can't help you further, but i guess worst case scenario you'd have to have her wear light, long-sleeve blouses/shirts, a uv-cap and try to keep her out of the sun as much as possible.