Before I was diagnosed with MAC & bronchiectasis, I was treated about 4-5 times over a period of 3 winters for H. influenza - each time a single course of bactrim or a similar antibiotic made me feel better, but the next cold would immediately progress into bronchitis then pneumonia again. It was a followup to are particularly nasty bout that led to my diagnosis & two years of treatment.

Do you do daily airway clearance to help keep your lungs healthy? Since the H. influenza can persist, just like MAC, it might help to avoid a recurrence. I don't know if a saline neb would help disable the H.I., but you could ask your doc.
Sue