The Burt's Bees Defense ointment will help since its main ingredient is zinc oxide. This isn't the same Doctor's Defense Zen Fusion ointment that several posters have spoken about favorably here, though. That Doctor's Defense is an ointment with Chinese herbs in it. Here is their website:
Doctor's Defense is soothing to skin with eczema, and it helps to heal the eczema outbreak more quickly than it would if left alone, but it's not a cure. It's important to identify what is causing the eczema to begin with for lasting relief, or otherwise the underlying condition causing the eczema will bring about another eczema outbreak.
We are very lucky that so many posters have added their thoughts to this thread. It's a wonderful thread with so many helpful suggestions--one of the best!