Auma Obama was being interviewed by CNN in the middle of Tuesday's protests in Nairobi, Kenya -- when all of a sudden, explosions could be heard in the background ... and she starts coughing and tearing up.

The ex-Prez's half sibling -- to whom he's related on his father's side -- says she can't see anymore because of tear gas in the air ... and CNN field reporter Larry Madowo starts coughing too as the street interview is forced to end.

Before police unleashed tear gas on protesters outside parliament, Auma  -- a Kenyan activist -- told CNN she was at the demonstration to show the world what was happening to the young Kenyans demonstrating for their rights with flags and banners.

Widespread protests are breaking out in Kenya, where citizens are pushing back against a controversial new finance bill, which includes proposed tax increases.

Reports out of Nairobi say police opened fire on protesters who tried to storm parliament after tear gas and water cannons failed to disperse crowds ... with at least 5 people shot dead and dozens more wounded.