Sorry to hear Boris is ill! With regards to a URI, its good he is on antibiotics promptly. Keep him warm, away from any drafts and a bowl of boiling water with albas oil in next to his cage (out of piggies reach) should help clear his nose. Weigh him daily at the same time in the feeding cycle, any 50g + drop in a day or a slow steady decline in weight, top him up with syringe feed. Give little and often, as piggies with heavy breathing are at a higher risk of aspiration. Try giving his veg torn up in a deep plate with water poured on, as well as offering extra cucumber throughout the day. This will keep his hydration up, without the need to syringe water as, again, this can be dangerous when a piggy has laboured breathing.
Heart issues can be difficult to diagnose. If your vet (or the specialist) cant see any fluid in his lungs then its less likely to be a heart issue. Heart problems dont always create fluid, but since your piggy is presenting with URI issues, any potential heart issues would likely have fluid in the chest to be able to mimic his symptoms.
If you arent happy or he doesnt improve in the expected time, pushing for further investigations for a heart issue would make sense. Keep in mind that sedation or anaesthetic should be avoided if a heart issue is a possibility. Scans and xrays can be done consciously (none of my girls have ever been knocked out for any of those procedures).
Baytril can be hard on the guts good bacteria, so it is usually advised to offer a probiotic 1-2 hours after each antibiotic dose. Examples include fibreplex, dosed at 1 unit per kg of bodyweight, pro-c and avipro plus which are dosed at around a 1/3-1/2 scoop on damp veggies or syringed in water (avoid this route if you can in his condition).
@helen105281 and i both have heart piggies that are still going strong, if you need any advice on that front just tag us and we will help best we can.
Sending healing vibes to lovely boris xx