Hi, When I search for BE/NTM centers in Connecticut I came up with the following list. I do not see Yale or Brigham on the list. I do see NYU Langone. I trust this list. If it were I, I would choose two locations and make appointments. Expect wait time until you can be seen. Keep calling to see if there's anything sooner. They get cancellations all the time.

Show this list to your PCP tomorrow. Perhaps they know someone at one of these locations. Ask your PCP if it's helpful to have a local pulmonologist. Perhaps the PCP will agree to see/treat you if you have a flare in-between visits to the BE/NTM center, possibly making a local pulmonologist unnecessary. Also, ask this question of the BE/NTM team once you are seen. Sometimes local pulmonologists are willing to work with remote colleagues even though they are in different systems. Another question to ask.

Regarding finding an immunologist, also ask your PCP. All allergists are also trained in immunology but they might not specialize in immunology. Immune disorders are rarer than allergies, so allergists do not see these as much as "regular" allergies. Allergists, however, can order immune panels for screening purposes. Lab work might include IgG levels, Ig subclass levels and pneumococcal titers (6 weeks after getting the vaccine). They may also be willing to order genetic testing to rule out CF or immune deficiencies or autoimmune disorders.

Until then, read up on and start airway clearance, which is the mainstay of bronchiectasis treatment.
https://www.bronchiectasisandntminitiative.org/Find-Care/Care-Center-Network/Find-a-Center