Does my guinea pig have an upper respiratory infection?

The wheezing/labored breathing isn't normal. The only way to really know if it is a URI as compared to some simple allergy or other nasal passage problem is to have a vet listen to the lungs. Going off feed is a late symptom of illness and it is often too late to help by the time it happens. In this case, better safe than sorry so a trip to the vet is in order ASAP. Sooner would be better but you should still be OK in 24 hrs - don't put it off longer