Another book I forgot to mention was FROST by Marianna Baer. I very much enjoyed that one. Creepy without being overtly supernatural.
What you're talking about is more grotesque than Gothic, though the grotesque is certainly an element of Southern Gothicism. No, you don't need to have supernatural elements, just be aware that supernaturalism is part of Gothicism in general. For instance, several of Poe's stories aren't supernatural at all. The difference between Southern Gothicism and classical Gothicism is that in traditional, the supernatural is just there and designed to elicit the reader's emotional response. In Southern Gothicism, the supernatural is used as a commentary on social issues. If you don't want to put in a supernatural element because it would be shoe-horned into the story, by all means don't do it. As long as the other Southern Gothic elements are in place, you'd be all right. I'd read some Shirley Jackson and Flannery O'Connor for reference points.
Someone asked if there are any Gothics set in rural England. I haven't read many YA ones set in rural England. Most occur on a large manor or boarding school. IMMORTAL by Gillian Shields is one such book. A non-YA example would be JAMAICA INN by Daphne du Maurier.
My editor and I joke that my book is a northern Gothic, many of the hallmarks of Southern Gothicism but set about as far north in Wisconsin as you can get during a bitter, cold winter. That one is a Gothic paranormal romance and deals heavily in societal outcasts. The current book I'm writing is non-paranormal but very much a Southern Gothic horror. My agent and I agreed that the story can give the illusion than something supernatural may be going on but isn't. It's brought out in the characters' beliefs and superstitions.
