as they conveniently cut away.
Here's the full video.
Her coughing starts at :36. At :51 she asks for water. She heads for the front of the plane and at 1:11 you can clearly see her "handler", the mysterious big black guy, get up from his seat. At. 1:25 he unties the curtains dividing the sections of the plane and closes them. I have no idea of why he does this because they're made of see-through mesh. Hillary is behind a solid curtain in the front of the plane.
At 3:47, one of her aids tells the press that they're getting ready to land. At about 4:26 Hillary returns and reminds the press that she suffers from seasonal allergies and had the same problem last Labor Day.