Cold / Acute Bronchitis or Flu-should I be taking antibiotics? Please help!?

A couple of weeks ago I started with nasal drainage in the back of my throat. Then I had a dry cough that was brought on by pressure in the chest-up to my throat area thus hard to resist coughing. This turned into coughing up some hard chunks of whatever and it really hurt. I then went on a bikeride on a beautyful Sunday but the air was cold and I could feel my chest and airways burning. The next day it all turned into a terrible chest cold or bronchitis. I don't know. Everything feels swollen and my throat and airways were burning. My nose is extremely stuffed up and I think I had a low grade fever. Today I went to the doc and she prescribed z-pack antibiotics. Should I even be taking them? I now caugh up yellow/greenish flemme that isn't hard anymore thus hurts a little less. My nose is runny and it seems like I can blow it a lot. My cough sound scratchy and is being pushed out because the urge/pressure to cough is still there. Any suggestions? I am supposed to be on a 9 hour flight on the 28th. I question if I need the antibiotics and will they slow my recovery as they kill my good bacteria as well? Any advice would really be appreciated. Thank you!