Sounds good and you should stay on top of it if you keep your child moisturised morning and evening. If a flareup occurs and does not reside wet dressings and prescribed ointments and creams from your healthcare professional combined with a treatment plan (see my advice - Basic Eczema Treatment Plan) and much of your symptoms will be reduced.
Good tips on how you manage your childs mild eczema. If you are seeking further advice on this topic please place your posting in the Q&A section of this website and you will get prompt and plentiful advice from those who have travelled the road before you.

Yup it annoying but it could also be food allergies that actually bring it out get him tested and see what he is allergic to even mildly as this will come out on the skin known as ezema

My son had a patch on his cheek. I went to dermatologist and was diagnosed with eczema. I can't remember the medical name, but I remember the doctor said about white eczema. He prescribed my son with Fatty Ointment called Advantan. We only put it on (as the dermatologist recommended us) his cheek if the eczema appeared and don't put on if it goes away. It worked though, the skin went back to normal again after few days. It may appear once a while, I notice usually when he got flu or had spent too long in the shower and we just put the ointment back again. When his skin normal, I just give Cetaphil lotion to keep the skin moist.
I hope this could give you some idea. Good luck.