My daughter also have eczema since she was born and finally she is recovered since July. Her inner side of elbow, knee cap and ankle used to have raw skin exposed with some secretion. Her skin was never felt like a baby skin (always rough and flaky). Her condition has improved significantly overnight and it was amazing.
What I have done was using the "Gold silver flower stems" (directly translation please, sorry can't type chinese) to boil water (i used about 20 slices on 4 litres of water and boiled for 20 mins). Use that to mix with cold water to give your baby a bath. I also boiled some Chrysanthemum flowers and use it to clean the affected area 3 times a day. Make sure you pat dry after doing that. Apply aqueous cream 3 times a day (always after shower or when I clean her with the Chrysanthemum flowers water). Last but not least, I use a cream called "Elomet". You should only use it if the skin still show rediness or when it start to turn red again. Put on a very thin layer once a day (best to do that after shower or before they go to bed) and don't put on longer than 3 weeks (actually it only take me one week and she is all well). Make sure they don't lick it as it is medicine and harmful if swallow.
Now, my baby girl's skin is finally like a peeled hard boiled egg skin. So smooth and pretty. Also, I noticed that since then she can slept thru the night for 8 or 9 hours more with no problem. Just to keep her cool is the key.
Hope this easy and cheap alternate option can help everyone!