My daughter, age 16, is what is known as a good kid. Yet so often she literally does not see a mess she has made that I then have to clean up.
Example: she makes her own lunch in the morning, which is a good thing. BUT she invariably throws the wrapper for the cheese on the floor and leaves crumbs on the counter. Once or twice is not a problem as I can suggest she remember to finish the job, but the constant occurrence, five days a week, in spite of my asking her to watch what she is doing gets on my nerves. What it says is that she is not really thinking about the task she is performing or the fact that she lives with others.
Now, granted, your mom was probably having a bad day, hence the bad words, but your gaffe may be a symptom of a more pervasive problem not uncommon to teenagers (and husbands, by the way). That is, your putting dirty clothes in with clean shows that you aren’t paying attention. Then your mistake comes after “She was complaining all morning for me to take my laundry downstairs.” That means she is already frustrated.
A suggestion or two: first do what she asks when she asks it, coupling it with a cheerful response such as “Right away, Mom!”); her having to ask you again and again probably didn’t help her mood any.
Second, pay attention to what you are doing so you can catch the details; she may even have wanted you to bring your stuff down earlier so she could do one big load (and save water!) instead of several small ones. Instead, you put your dirty stuff on stuff she had just washed, creating more work instead of less.
Third, as others have said, surprise her by doing more than you need to, or doing chores before she asks you to do them, or by thanking her for something she has done for you.
In the “good old days” your mom wouldn’t be asking you to bring your laundry down or help clean the house or even to go to school, because you would be outside somewhere trying to earn a living and possibly supporting your own household. Enjoy the fact that you have the luxury of not having to be a full adult yet, but surprise and please your parents by showing them how adult you can be.