Hi - you may want to try the following (there's absolutely no pain or cost in trying it - it worked for both my children who had very bad infant eczema).
First, try to remove all artificial flavourings from your child's diet especially strawberry and orange and other fruit flavours (so no flavoured yoghurts, ice-cream etc) - also in medicines (try not to use calpol strawberry or orange) and things like flavoured toothpaste. Also avoid real strawberries and other sharp berries. Second, remove all scented items from your child's and your own use eg: scented wipes, nappy sacks, handwashes, soaps, detergents, candles, air-freshners, room sprays, diffusers etc. Also get rid of all antibac stuff, sprays etc. In addition, keep natural scents (esp lilies, roses, candles., diffusers etc) away from your child. Finally do not swim in chlorinated water until the eczema disappears.
With the above steps my kids' eczema disappeared in afew days. When they occasionally ate, say strawberry ice-cream on a few occasions, you could see the latent eczema patches start to re-appear. They have never had any skin problems since, nor any allergies.