Hello, sugar gliders are not likely to get the flu, the flu virus being restricted to birds, pigs and primates. However, they can have respiratory infections and allergies.
Swollen eyes are more often the result of either sinus / eyes infections, in which case antibiotics would be the course of treatment, or of tooth abcess (which is unlikely at such a young age).
Sneezing is a sound sugar gliders owners often hear and is not usually linked to sickness, they actually sneeze in their hands when grooming themselves.
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