Are there any first-person accounts by a child that had a similar experience as Bruno or Shmuel during the same time period?

There are a number of first-person accounts in which people reflect on their childhoods during the Holocaust. Some of these are from the perspective of German children and their relationship with this terrible period in history, and many are from the perspective of Jewish children.
For stories from the perspective of German children, I recommend Kriegskinder by Frederike Helwig. This book is a collection of the memories of several Germans who grew up during the war. I think you will find striking parallels between Bruno and Niklas Frank, who was the son of the Nazi governor of occupied Poland. Frank also published his own documentary "My Nazi Legacy: What Our Fathers Did."
There are also numerous memoirs from the perspective of Jewish children who survived the death camps. A very compelling one would be Eva's Story by Eva Schloss. This harrowing and detailed first-person account tells the story of how a young Jewish girl survived the daily humiliations and dangers of Auschwitz. It also deals with how she and her family attempted to hide before their arrests and how they dealt with the aftermath of liberation.