Hi
Mucus in the eyes and nose is a symptom of a well developed un- or under-treated bacterial respiratory infection in the upper respirator tract (URI - sinuses, throat and bronchia); that is also where the crackling and rasping happens. Ideally, it should never get as far as ny mucus with prompt treatment.
If the problem sits deeper (in the lung, which means a lower respiratory infection, or LRI) there will be less sound. Sometimes, a clicking in the chest/lung area is the only indication of a pneumonia (or rather a fluid build up in the lungs) apart from more laboured breathing.
Your vet is doing the sensible approach to address first the more easily ruled out problems (a respiratory infection) before tackling a potential heart problem, which can pretty difficult to diagnose; as I know from my own piggies. Please conduct the full course of antbiotics and review if there is no change by the end. Antibiotics take several days to build up to full efficiency and then fade again over several days after the end of the course.
Please switch from the usual on weekly weigh-in on your kitchen scales to weighing daily first thing in the morning for best day-to-day comparison (the daily weight swing of about 30-40g is always lowest by then) and so you can plan any level of support for the coming day. The need to breathe comes before the need to drink and only thirdly the need to eat; that is why laboured breathing comes with the potential of a dimished or lost appetite. You cannot check the hay intake by eye but it makes over three quarters of what a piggy eats in a day. We speak of weight loss from 50g onwards - just the difference between a full and an empty bladder is 10g!
Add to that the potential appetite dampening effect of an antibiotic and you can understand why any breathing issues can come with a double whammy on the appetite. Right now, you just want to keep an eye on it with your weighing so you can step in with top up feeding when actually needed.
You can try and soften the impact on the gut with free 'poo soup' and/or a probiotic. Either give the probiotic 1 hours before or 2 hours after the antibiotic.
Probiotics & Live Gut Microbiome Transfer ('Poo Soup'); Recovery Formula Foods And Vitamin C: Overview With Product Links and Transfer Recipe
All the best.