"Aggravating" is a good, standard English word. The verb form is "to aggravate." The noun is "an aggravation."
Ellen uses it to mean "annoying" or "irritating." In this case, "aggravating" refers to an unpleasant emotion that is like anger, but not as strong. This is slightly colloquial usage.
The old, original meaning was "to make something worse."
There is a technical legal phrase that often occurs in news stories, "aggravated assault." This refers to a number of different crimes that are worse than "simple assault."
"My mother used to hum at night" is a great example of something aggravating. It might bother some people and not others. It bothers Ellen. She only feels "aggravated," not "angry" because her mother isn't trying to bother Ellen.
Some examples of usage found in a Google Books search include:
"She did not want or need this aggravating man's approval."
"I get aggravated doing my kind of work, too,” said the man. “When someone aggravates me I go home and do my mosaics in the bedroom. My wife sees me and says, 'What's aggravating you?'"
The American Heritage Dictionary has a usage note: "It is claimed by some that aggravate should not be used to mean "to irritate, annoy, rouse to anger." But such senses for the word date back to the 17th century and are pervasive. In our 2005 survey, 83 percent of the Usage Panel accepted this usage in the sentence: 'It's the endless wait for luggage that aggravates me the most about air travel.'"