Why do we sing those crazy ?/mi/ and /ni/ sounds in lessons? 
Here’s some really cool research on humming and sinusitis:
Healthy sinuses have a high concentration of NO (gaseous nitric oxide) production.
NO is known to be increased 15- to 20-fold by humming compared with quiet exhalation.
NO is known to be broadly antifungal, antiviral and antibacterial.
One case report shows that a subject hummed strongly for an hour at bedtime the first night, and hummed several times a day for the following 4 days as treatment for severe chronic rhinosinusitis (CRS).
The morning after the first 1-hour humming session, the subject awoke with a clear nose and found himself breathing easily through his nose for the first time in over 1 month. During the following 4 days, CRS symptoms slightly reoccurred, but with much less intensity each day. By humming 60-120 times four times per day (with a session at bedtime), CRS symptoms were essentially eliminated in 4 days.
The article hypothesized that strong, prolonged humming increased endogenous nasal NO production, thus eliminating CRS by antifungal means.