What if Bucky had adopted a small child during his time in Bucharest? He knew the risks of having a small child around someone as dangerous as himself but the poor kid was sitting outside his door, curled up to their own shirt to keep themselves warm. Bucky had to take them in, he associated the child with Steve, he couldn't let this child go.

Bucky walking into his apartment and thats why he's so defensive inside his house with Captain America is inside it with him and fear spikes in his chest thinking that his child will leave him for the hero. His child knew that they were being followed by the police and thats why he fled so quick from T'Challa, his child was allergic to cats and he couldnt have "cat" fur all over him.