Yes, this definition is correct for the context. As you state, the definition is
To maintain composure; to avoid an overly emotional reaction; to suppress an instinct or urge.
Later on in the text, it states that she "tries to slow her breathing, the way she's been taught. To stop the images from coming back, from taking over". Also, earlier, there is background given that Riley has been deployed to Afghanistan.
She reminds herself she's not in Afghanistan anymore. She's home, safe, in New York state.
Based on this context, the author is trying to convey the fact that Riley has Post Traumatic Stress Disorder. Some symptoms of PTSD include extreme emotional reactions and intrusive memories of the event.
When the author mentions the "images", this is most likely referring to the intrusive memories, or the things Riley has seen that has distressed her in some way while she was deployed in Afghanistan.
Finally, to tie this point to your question about the definition of "keep it together", the second symptom I mentioned is extreme emotional reactions. Look at the definition of "keep it together" again.
To maintain composure; to avoid an overly emotional reaction; to suppress an instinct or urge.
Therefore, when Riley is "keeping herself together", she is consciously making an effort to not break down because of her PTSD.
Best Answer
Way back is used for 'long ago'. Check OxfordDictionaries's entry
Your sentence sounds strange to me with those words in it. Don't use it that way.
Probably, you are confused with this -
So, read the entry and clarify your doubt! :)