My daughter also has eczema so to avoid break outs and b/c I felt she was too young for sunscreen, I used physical elements as protection like cotton/linen long sleeve and pant clothing, shades and hats. But I am told that mustela is a good brand. Also here are some good guidelines for your sun protection review:
Use a water resistant sunscreen with an SPF of at least 15 to 30 that provides broad spectrum UVA and UVB protection.
Other characteristics of the best sunscreens and sunblock for young kids include that they are hypoallergenic and fragrance free and come in a form that is easy to use on your child, whether that means it is a gel, lotion, spray, continuous spray, etc., so that you will actually use them.
Apply enough sunscreen to protect your child.
Use sunscreen even if it is cloudy outside. Clouds don't absorb all of the UV radiation that may harm your child.
Avoid sun exposure when the effects of the sun are the strongest, which is usually from about 10 a.m. to 4 p.m.
Use physical protection, including clothing, such a hat with a 3-inch brim, lightweight long pants and long-sleeved shirts, and/or a stroller, tent, umbrella or tree.
Encourage your children to wear sunglasses that protect against ultraviolet rays.