Chillsey,
I'm so sorry you have to be here, but so glad you found us. I, too, have a 77 year-old mom with NSCLC. In fact, she also has a 3 cm tumor in her lung.
I can't answer your questions about the coughing and shortness of breath as, so far, Mom hasn't experience that yet. There are pleny of people here who will do their best to answer your questions with their experience.
It might be helpful if you could post information about your mom and her diagnosis in your profile. That way people will know better how to respond to your questions.
The first thing I suggest is to stop using the word "terminal" and to seek a doctor that will treat her aggressively, if that is what she wants. There are many people on this board who have had that word flung at them and I'm happy to say that they flung it right back and have exceeded all expectations.
Peace,
Susan