I' m sorry to hear you are struggling with bronchiectasis and have no luck coughing up the mucus. Going to an ID doctor is the right move. I had MAC 11 years ago and have been free of it since taking the Big 3. They work. Do not be afraid of antibiotics. The infections can spread insidiously while you feel good. While I am able to get 95 % O2 with one dead lobe and another compromised, I would not suggest ignoring a specialist's advice. Since I was diagnosed, many more pulmonologists have become educated about it and more research is being done. You are lucky to have them available.
About your mucus. I use postural drainage, the flutter valve and nebulizer twice a day. I agree with @pacathy Good luck