You are right. If this was an acute incident, then she should have jumped in the ambulance and gone to the hospital since she showed every sign of having a serious case of pneumonia (and pneumonia in a senior citizen is very very dangerous).
Instead everyone seems to want to brush it off, since everyone knows this is a chronic problem (probably related to congestive heart failure or COPD) so they pretend it's nothing and she's perfectly healthy.
This has been going on for months now. She is definitely sick.
Based on comments from a medical doctor, I believe the coughing is caused by a heart arrythmia, and that she is minimizing or refusing treatment because it would impose restrictions that would force the campaign to end.
I wonder if she feels uncomfortable when Obama gives an interview about handing out free tampons or pads to students?