It sounds like what your talking about is Tracheomalacia or Laryngomalacia.
My LO was diagnosed w/ Tracheomalacia @ 1 wk old. It's sounds scarier than it really is. You can google and find out alot of info on these. My Dr. told me that cartilage all grows at the same time so you'll know if the cartilage in the throat is getting firmer by feeling her ears and nose cause they all firm up at the same time. My Dr. is funny also and he was telling me we'll be spending alot more time defending what our LO's have, cause grandparents, friends, strangers are all gonna look and ask questions. NON STOP!!!. But just know it's not too serious. :)