Oh gosh, poor little guy and poor mum too! Hop over to allergy forum! You will get lots of sympathy from sleep-deprived mothers trying to keep their kids on the growth chart and skin intact.
My son could not sleep until his allergies were under control and that was 2.5 very bad years with infected eczema and eight different doctors. Before his eczema showed up, it was very bad sleep, a lot of fussing and crying, arching of back (because of food allergies and bad tummy), very gassy stomach, and constant rubbing of skin. At night, he latched on desperately but did not always nurse properly. It was more like a fitful sleep, whine a little, nurse a little, go back to sleep and it starts all over again. I didn't understand it at all and I really resented it and blamed it on a difficult temperament and it's really really hard to think straight and function after months of sleep deprivation.
I will not go into the range of medications we used, and we had many bad doctors along the way who simply handed out steriod creams and told us to hope that he will outgrow it. He has a combination of food and environmental allergies leading to prolonged fungal and bacterial infections from age one that were very difficult to clear. But when we finally found the right doctor through friend of acquaintances (we were desperate) - i cannot tell you the relief of having one night of unbroken sleep. I realised then that my little guy was really as tired as I was. He slept 11 hours straight (first time since birth) and when he woke up, his appetite was good! He was two plus by then, so we were both really really tired! He is four now and recently had another flare-up and has been on antibiotic cream for three weeks - much longer than the typical patient and his doctor had to tweak his management plan because his skin is so raw. I am flushing his skin with saline many times a day and hotwashing all his beddings twice a week as well as going on a restricted diet and thank goodness his patches are starting to heal again and he is just waking up twice a night now to ask me to help him rub instead of screaming and crying from the itch and pain.
I will say focus on the eczema instead. When he can sleep well, he will eat well. If one doctor doesn't help, try another. Our doctor goes against all the usual eczema management plan and does not advocate using moisturiser. But I think it's also because of the kind of cases he gets where there is usually prolonged infection from earlier mismangement. If your son is still at the early stages of eczema, the usual route will be to moisturise and to hunt down the triggers. If there are no gastrointestinal issues, you should look into environmental triggers. Common ones are pet dander, dustmite and pollen.
I know I am going totally off the gifted children topic, so I will stop here. You will find lots of info at the allergy section, good luck!!