Please contact the vets again. However, if Sylvester is behaving like normal, is eating and well and holding his weight, then he is not seriously ill. it may just be that the antibiotic is suppressing the symptoms but not curing them because there is a different reason. You may want to discuss with your vet where to go from there.
What kind of hay do you feed; is it dust extracted or not? could you try another brand to see whether that is making a difference?
A Comprehensive Hay Guide for Guinea Pigs (incl. providers in several countries)
Have you considered any perfumes, air fresheners, scent sticks, dry radiator hear or air conditioning etc. which can all influence the breathing? It is generally a slow elimination process when you have to work through environmental factors.
Guinea pigs have a very small resiratory tract with narrow airways. that means that you can hear every little obstruction somewhere; they also can't breathe through their mouths, which means that even a mildly stuffy nose can sound quite impressive.
The need to breathe comes before the need to drink and only thirdly the need to eat. That is the reason why a serious respiratory problem is always connected with a loss of appetite and rather quickly lethargy from lack of fuel and the effort to breathe.
Weight management and health monitoring tips:
Weight - Monitoring and Management