I have no idea where the ideas of limbo and purgatory originated. The Bible is very clear that man is condemned because he rejects the revelation that God gives of Himself to everyone, through His creation, through people's consiences, and through the direct, special revelation of the Gospel (the revelation of Christ's sacrifice for man) (Romans 1:18-32). I don't imagine babies have any capacity to do this, so they would be in heaven.
I'm convinced that Scripture cuts to the truth of, and remedy to, the human condition (that is, sin itself), far more powerfully than any system of theology can. (1 Corinthians 1:19)