I think it's safe to say that the cheeseburger isn't sitting well with her right now. I really don't think these little guys should eat ANY people food other than fresh veggies, some fruits, plain boiled chicken, cottage cheese, etc. Their digestive systems are too delicate for the kind of crap WE put in our bodies.
Honestly, if she's acting listless and wont eat, I'd call the vet. It's one thing if she wont eat and her tummy is gurgly (diarrhea), but if she's really lethargic then I'd be worried about her. You didn't mention if Kaci was the 3mth old or the 7mth old - if she's only 3mths, then she can't really afford to miss a meal I imagine.
Keep trying with the syrup and call the vet to see what they say.
Welcome to YT!