Putting the issues with co-workers, managers and docs aside for a moment-The way you refer to your patients does indeed make me think you chose the wrong field. You complain that they are old, sick, demented, indigent, obese...who did you think you would be taking care of, the young, sane, wealthy and attractive?
Illness can do funny things to people-it renders them helpless, fearful, vulnerable. Same with family members. Often those feelings get channeled into anger and resentment, which are then hurled at you because you are the convenient target. It is hard not to take it personally. It is hard not to get burnt out. But if you have only been doing it for a little over a year, and you're already burnt out to the point where you are dreading waking up in the morning, where you have no compassion or empathy (with the exception of those patients you deem as both "truly sick" AND appreciative of your help) , then yes, it's a good possibility you are in the wrong field.
And that's OK! The great thing about nursing though is that there are many things you can do with your BSN that don't require you to be at the bedside. You might consider case management, informatics, or another specialty that doesn't involve direct patient care. With your interest in nutrition, perhaps becoming a diabetes nurse educator would be a good fit. Moving to another floor or hospital isn't going to solve your problem-there is no specialty in nursing where you aren't going to have to deal with ungrateful, unmotivated patients and you don't seem well equipped to handle them. Better to learn that about yourself now, early on in your career, and go find something that makes you happy.
Best of luck to you!