Whether your dog is normally "calm" or not, there's a very good chance that she was chasing livestock, particularly as a young adolescent dog. Animals run from unfamiliar dogs, and dogs chase things that run. And if she did chase your neighbor's animals, they're within their rights to shoot. Even if a dog doesn't bite an animal, stress reduces productivity and profits. Ranchers have the right to protect their livelihood. And, since your dog was running loose and you didn't see what happened, you've no way to prove anything either way and reporting to the police would be pointless. Your neighbor will say your dog was harassing their stock, and that will be the end of it. Take your dog to a vet if you haven't already, and do what's feasible for her after the vet has assessed her (euthanasia or treatment).
If you get another dog (or this one survives), you need to do a better job containing them. I grew up in a rural area where the sheriff's response to stray dog complaints was to tell you to shoot them. Protect your pets by appropriately confining them. People move to the country and think their dogs should be free to roam, but it's even more important to keep them on your own property in a rural area.