Okay, so, at the end of The Hunger Games: Mockingjay, it says, when Katniss and Peeta were making that book with pictures of their dead family and friends, “Pictures of Finnick and Annie’s newborn son”.
The line you quoted (from the end of Chapter 27) is the first time we hear of their son.
Finnick and Annie get married in Chapter 16 and Finnick dies in Chapter 22, and it's almost guaranteed that the child was conceived during this period. It's hard to say if Annie even knew that she was pregnant when Finnick was alive. And not much time passes between then and Chapter 26, and during some of that time, Katniss was unconscious.
In Chapter 26, when Annie and Katniss see each other, Katniss doesn't mention anything about Annie's appearance so it's likely that she doesn't look pregnant. It's still not clear if Annie knows or not, but it's certainly not a good time to bring it up if she does.
That's right before Katniss kills Coin. After that, Katniss is locked up as they decide what to do with her, then sent to District 12, where she doesn't pick up the phone. There was no good way for the information to get to her, especially since Annie and Katniss weren't that close (which we know from Chapter 16, before the wedding: "I'm a little leery about being with Annie since all I really know about her is that Finnick loves her and everybody thinks she's mad").