That’s a frustrating situation! But I actually think you were right not to mention being sick at the interview. It could sound negative, like an excuse even before it starts, and also the interviewer might wish not to be exposed to a cold or flu! Your best choice at the time was either go ahead and not say anything (which you did) or reschedule.
Now, I suggest waiting for the application decision. The application is what it is, and schools would not appreciate additional info regarding the app at this point. Then, if you happen to be
wait-listed, that’s the time to mention that you believe the interview didn’t go well, and to discuss the positive steps you’ve taken (here too I suggest not mentioning you had a cold, which would sound like an excuse). Keep everything affirmative, positive, and forward-looking.
Good luck! I commend the constructive steps you’re taking.