I'm ashamed of the motherly feelings I've developed toward a kid where I work.
How did you develop those feelings?
I've developed a friendship with the kid's father so it might be because of that, or maybe I just feel that way because the kid is likeable.
If your job consists of caring for other people's children, then it is good to feel love and kindness toward them. You probably shouldn't favor a child over other children because you like that child's father, though. That would be unprofessional.
But I want to be friends with the kid.
There's nothing wrong with wanting to care for a child, but you shouldn't favor one over another. You should also be careful not to cross any boundaries since you aren't actually the child's mother.