Flustered:: to make (someone) nervous and confused (Verb)

Source http://www.merriam-webster.com/dictionary/flustered?show=0&t=1386688017

“I found these letters deeply absorbing; not only did hours pass without my noticing,  so that I often found myself huffing, flustering to pick up my son, but often it felt like sixty-two years had passed without my noticing–such was the ringing immediacy of Lucy’s voice.”

This shows just moving the letters of Lucy and Alfred were. They were moving Egan and making Egan nervous and confused that she often went to pick her son to  get a clear of mind.