Would an animal shelter take my dog? :(?

My dog is really sick, and has so much medical expenses we can't afford to take care of it anymore. It's 8 years old, and my dad just spent his last $300 on a trip to the vet recently, and as of right now he's not eating or opening his mouth from some new problem he has on top of bladder stones/ a chronic ear infection/ and collapsing trachea. He's telling me to call the animal shelter and bring him in, but i'm afraid that when i go there and sign him over, they're going to kill him. If they do that i'd rather take him to the vets and do it myself. I don't want him to be alone in a shelter if that is necessary. He's so sweet and it's so hard after having him since he was a puppy to give him up. But i guess what i'm asking is, would the shelter take my dog, fix him up and give him to a home that could afford his medical costs? Thats what my dad is telling me, but it seems unrealistic. My poor dog, he really doesn't deserve this :'(