TL;DR: No.
The line you're talking about is actually "I forgot everything you taught me".
What does the little girl say?
I don't know of any official scripts available online, and the dialogue you're talking about doesn't appear in the closed captions, so here's my own transcription this scene, along with what the closed captions on the iTunes version of the episode do say. The girl's name is Molly, and she was played by Kennedy Brice.
Carol: Molly!
CC: (Carol yelling)

Carol (to Molly): Come with me! (Carol pushes Molly to a nearby cell) Stay in here.
CC: Come with me. Stay in here.
Karen: (preventing a man from closing the cell door before Molly can enter) Wait, wait, wait, wait!
CC: Wait, wait, wait, wait!
Molly (to Carol): I forgot everything you taught me!
CC: (Sobbing)

- The Walking Dead Season 4, Episode 2, Infected
This line is quoted on the TWD wiki, it matches what we hear in the clip, and it makes sense: in the previous episode -* 30 Days Without an Accident *- Carol was seen teaching Molly and the other kids how to kill walkers:

Molly was simply explaining to Carol that she didn't remember what Carol had taught them.
The word "zombie" in the Walking Dead universe:
The shows:
On the shows, the word "zombie" simply doesn't exist.
The comics:
It is used - but only very rarely - in the comics; I have only been able to find two instances in which a character says "zombie":

- The Walking Dead, Issue #2

- The Walking Dead, Issue #7
Other media:
The word "zombie" has also appeared a few times in the Walking Dead games from Telltale Games, but the only Walking Dead media in which it is used frequently are the print novels. I only have the first volume of the series of print novels, but the word "zombie" appears 76 times in that book alone:
Why don't they say "zombie" on the shows?
We have word of god here, from the creator of the franchise, writer of the comics and novels, and Executive Producer of both shows, Robert Kirkman:
One of the things about this world is that people don’t know how to shoot people in the head at first, and they’re not familiar with zombies, per se. This isn’t a world the (George) Romero movies exist, for instance...because we don’t want to portray it that way, we felt like having them be saying ‘zombie’ all the time would hearken back to all of the zombie films which we, in the real world, know about. So by calling them something different, we’re kind of giving a nod to … these people don’t understand the situation. They’ve never seen this in pop culture, this is a completely new thing for them.
- Robert Kirkman on Talking Dead S1E2, Bloodletting, quoted on The Wrap
Related:
What are all the different names survivors have called zombies?
Has anyone revealed why the word “zombie” is used in the comics, but not on the show(s)?