MC gave the baby milk to Dietrich because that was the only food she got, and Dietrich got none. In the novel it said that the newborns got that milk and it was made to have all the nutrients you needed for growth and development. Dietrich has been hunting for his own food since no one was taking care of him and he isn't a baby anymore. MC wanted to give Dietrich the milk because he's still a growing boy and needs more nutrients to grow big and strong, especially in that succession competition.
Also in the novel the MC actually says that she doesn't want to cry that much but her physiological state of a baby means she can't mentally handle the complex emotions and therefore cries as the way to let out the emotions.