Hi @cila,
The link that @johnbishop provided also lists the phone numbers to call for each Mayo Clinic location, as well as tips and frequently asked questions about requesting an appointment at Mayo Clinic. You can either self-refer or have your physician make a referral.

It sounds like you’ve already called several times, but are not getting the response you're hoping for. Other members share their tips in this discussion.
- Can't get an appointment: Any tips on what to do? https://connect.mayoclinic.org/discussion/cant-get-an-appointment/

Mayo Clinic has more requests for appointments than available openings in some departments. Have you been told that Sleep Medicine is unable to accept new patients at this time? Are you already a patient in Pulmonology for MAC and Brochiectactsis? Which location have you been calling?

In order to not take this discussion to far off-topic, please send me a message using this form https://connect.mayoclinic.org/contact-a-community-moderator/