I would ask for RAST blood tests - it brought up major allergies for DS at 6 months. He was raw with eczema, had reflux and was having hives. We were put on neocate formula and he stayed on that until 4, when he grew out of his soy allergy.
Here are some things that helped him through it -
Daily baths with oilatum junior - Derm told us that it was more important to reduce the bacterial loading, than the risk of drying the skin. Dermol in bath if really bad. Gently pat dry, but leave some water on skin and apply Epaderm generously. At 6 months- we were doing it every 2 hrs. With a six yr old - I would suggest before school, on pickup and before bed.
Now DS is healed, we use E45 bubble bath for a treat - with no issue.
We use Method laundry wash, previously used surcare but this is better for my DS and we use it for the whole family.
If his skin is raw, he my need antibiotics to bring it under control and heal. Along with stronger steroids.
Ultrasun sun cream seems to be the best for our DS - less sweating than others.
We use a USA brand for shampoo, conditioner and body wash - its free of chemicals and best of all does not leave DS looking greasy. It is expensive in the UK, but a little goes a long way.
www.amazon.co.uk/Pharmaceutical-Specialties-Clear-Conditioner-Bottle/dp/B0006FMK70/ref=sr_1_6?s=drugstore&ie=UTF8&qid=1429139133&sr=1-6&keywords=free+%26+clear+shampoo
Wrapping DS made him worse, rubbed and woke him up, we found using tighter PJ's worked for us. NEXT snuggle fit ones work brilliantly as an alterative, make sure they are the 100 percent cotton ones as they vary.
You may have tried some of the above, but I have just listed what works for us and it may give you some new ideas.
Also, at six you can go dairy free on your own (if he is not allergic to soy) - Alpro plus 1 soy milk had added vits / calcium and they do alterative yogurts, etc. You need to do it for a good period though, it took us at least six months to fully recover his skin. Talk to your allergist and they usually have a dietarian who can help.
It's quite late - so sorry it's quickly written.