Personally, I'd stay away from steroids until I desperately needed them, or if you are an asthmatic during a difficult flare. Instead I'd work to clear my lungs with hypertonic saline via nebulizer/compressor followed by breath holding and huff coughing. If your lungs sound gunky, have you submitted sputum for a culture? That's the only way to determine if you have an infection; stethoscope auscultation cannot determine that. Maybe you have something brewing that needs a targeted antibiotic treatment.

If bacterial infection has been ruled out, instead of steroids you might ask your pulmonologist about 3-day azithromycin, which is a macrolide that helps reduce inflammation in bronchiectasis. Before its use, however, any kind of NTM bacteria must be ruled out usually through sputum culture and CT scan. Are you seeing a pulmonologist who specializes in bronchiectasis?

If you don't have time to follow through on the above, in the short term I'd ask for scripts for albuterol and hypertonic saline for the nebulizer.