The "child" on the floor wasn't a part of Voldemort's soul. It was his afterlife. After he hit Harry with Avada Kedavra he almost got killed as well, so this child is what Voldemort going to become after he dies.
OMG WE ARE ALL GOING TO GO INSANE FROM THIS!!LOL
No,probably not but It could be the whole "piece of Voldemort's soul" thing I didn't think of that , most likely because I didn't read the firt 4 books.
I'm still a huge fan but I love the last 3 so much I read them over and over and over again.