I'm going to tell my housemate she's coughing too much
What is going on, was she sick? Why is she coughing?
She's making noise all the time. It pisses me off.
It's inconsiderate to get annoyed by your sick roommate. You should be kind enough to support her and see if you can help her so that she would stop coughing. It's wrong that you want to criticize her for coughing.
She's sick, what do you want? I'm fine with it.
I do not think you're fine with it if you think her coughing is annoying. If she's sick then she may infect you, so I think if you really need to you can visit other relatives or go to a hotel for a temporary stay so that you can stop being annoyed and also not risk yourself of getting infected.