Great question. Both can be used. But remember it depends on the specific sentence, this dictates the grammar structure. If you are referring to yourself, where you are talking about your childhood, sure "In my childhood will be the way to go - "In my childhood, we always watched the soccer game at the weekend".
When this is not starting a sentence, you will probably use In childhood, "Some people learn more effectively in childhood". Other variations, In his childhood, her childhood, during childhood, as a child.
But definitely when talking about yourself, just say (for simplicity sake) "In my childhood or "when I was little" I .... blah blah blah -:)
Hope this helped! Reach out to me if you need any more questions answered.