As long as her breathing sounds okay, she's probably just getting all that gunk up and out. Coughing and running nose, helps to get the congestion out.
I hope that she feels better soon. Luna had some kind of respiratory infection that needed two rounds of meds, then it got better. The second med was clavamox, and within 2 days of starting that her cough got much better

It helps to run a vaporizor too