your area is completely without birds of prey? that’s surprising. and you can’t count on predators behaving around prey. your dog is also a predator. he may be trained to leave the rabbit alone, but that doesn’t mean you should leave them together unsupervised.
is your rabbit not used to being handled? are you rough when putting him in the cage?
he needs a vet, Bria. please find a way to take him in, even if you have to get Care Credit or surrender him.
you have to think about HIS needs first, here…and not taking him to the vet when he’s obviously very sick is willful neglect.