No, no, no. There's no contradiction there. Chapter 10 is just an aside telling you how the different nations came to be from Noah's offspring, but that does not mean that chapter 11 continues the story from after these nations all come into being. That is an unreasonable assumption to arrive at.
Bible books aren't written in perfect chronological order. Writers often make chronological detours to make a particular point. Genesis 10 is a detour from the regular chronology of Genesis for the purpose of explaining human lineage from Noah. The main story thread runs from Genesis 9 straight into Genesis 11. Genesis 10 is like a fork that branches out to a separate story thread that explains human lineages from Noah. The timeline of that thread goes beyond the timeline of Genesis 11. But that thread terminates at the end of chapter 10.
There are plenty real contradictions and inconsistencies in the bible but what you mention in your first paragram, ain't one of them.