How to overcome fear of bunny's death?

Hey there, my bunny has respiration problems and i brought him to the vet. Today morning it seems like his problem got worst and i panicked and called the vet and all, but it wasn't as bad as it seemed, so i canceled the appointment and gave him his antibiotics, but now i think im regretting it. I dont know if theres improvement, maybe a tiny bit. But im just really sad hearing him breathing like that, and im thinking of all the worse scnarious which will happen. Im afraid this fear is making me nervous thinking about giving my bunny his antibiotics as he does reject it, which will make him nervous. I read that bunnies are good at sensing fear and sadness, which is probably what im feeling now. Does anyone know how to overcome this? and can i let my bunny out for his run even if he is breathing hard, i feel bad jailing him in his hutch. I really want my bunny to be fine, i want to be with him for a few years. I love him sooo much. help :(