I'm sure they suffer from all kinds of diseases and illnesses like all animals do. Not much you can do without taking it to a vet unfortunately.
Here is a list of common illnesses and symptoms, but as said above the only way to properly diagnose is to take it to a vet, respiratory infections are quite common and your symptoms point that direction but without a culture test and trained ear to listen to the lungs this can't be verified...
http://www.guinealynx.info/emergency.html
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