I feel like leaving the room every time my roommate has a coughing fit.
Why do you want to leave the room every time your roomate has a coughing fit?
It's a good idea for me to do so.
It's understandable you don't want to be around a roommate having a coughing fit but if you get up and leave the room every time that happens it might make them feel self conscious. Instead of getting up and leaving you should offer them a cough drop.
Not a bad idea. I'll cough on purpose to make it less awkward for me to have cough drops on hand.
I don't think you need to start coughing as well, just try to ignore your roommates cough.