I do happen to believe in ghosts, as I lived with one growing up in my house. It too was an old home, built in the late 1800's. I never considered it to be a demon, and it never did anything bad to us. In my case, the ghost was an older man. I am certain that he was the original owner of the house.
It could be quite possible the kid you saw was indeed the one that died. I think this is another perfect example of the fact we don't know exactly what happens after death. I personally do believe in heaven, but maybe heaven is different for each individual.
In will be interesting one day, many years from now, to find out.