When my oldest daughters were small - i am talking movre than thirty years ago, long before the current craze, and proliforation of homeopathy, both suffered severely with eczema, the youngest especially who had to be bathed and banadaged daily.
In desparation, their mum (before i knew her) took them to a local homeopath. Far from being a charlatan, he was hardly known at all - he only saw people by word of outh referral, and made no appointments, but everyone queued and was seen on the days of his surgeries, which could and did go on until the early hours of the morning.
He mixed some dark liquid of which both girls drank a teaspoonful twice a day. The yongest's skin erupted in sores and green puss, before clearing completely. The odest one's skin was less seriously affected, rashed up, and again, cleared - never to return in either of them.
My wife is about as cynical and suspicious an individual about 'miracle cures' as you woll find anywhere, but this was, and is proof that homeopathy works.
The practicioner contiuned until his death, never ever advertised anywhere, saw people no matter how long they waited on surgery days, and loads of people came from all over the UK, and abroad to see him.
I simply put forward this experience as a fact - everyone can make up their own minds - but i doubt you can use a 'placebo' on a four-year-old and expect success.