They're similar and quite synonymous, but 'jeszcze' would have a bit different meaning here. Although I guess that both would be probably translated into English the same way... I really don't know whether 'jeszcze' should be accepted or not.
"Wciąż jesteś dzieckiem" makes me interpret it as "You're still a child at heart, with your childish naivety and behaviour". It's like "you were a child, and your time as a child is not over yet".
"Jesteś jeszcze dzieckiem" sounds as a simple "You're still a child, you're too young for that". It's like "you are a child, you will be an adult, but not yet".
But these are of course just an individual's thoughts on the differences.
It seems to me that "Wciąż jesteś dzieckiem" is a bit stronger, but your version looks fine to me and it's accepted.
I don't know the exact spelling but with my colleagues I use in spoken language 'nadal' to express the word 'still', can this word be used here instead of 'wciąz'?