Sarah, Blackie was the same way, too, when she was first diagnosed. She'd just lay next to the water bowl, or close to it as possible. Her grooming wasn't there, and she was constantly tired, and lethargic. She used to play a lot before her ailment, but not now. Since I've started getting her regulated better, she's not nearly as lethargic, and she's grooming herself a lot more. She used to lay down on the floor alot instead of sit down. Now, it's more sitting than laying. She still lays down on occasion on the kitchen floor, but I think that's to do with the coolnes of the floor against her belly. It's still rather warm here in Texas. :lol:
I have noticed lately that when I need to feed her either a medium or a high carbed food, she does get that lethargic look about her, until the insulin kicks in, and brings her #s back down to where they need to be. She's a strict, no-carb food now (I feed her Evo 95% Chicken and Turkey, which is 0% in carbs, and she has steamed chicken as a treat 2x a day, which is also 0% in carbs). You do learn your cat as you go along this process, and you do become more vigilant with anything and everything normal or otherwise. Having a diabetic cat is a learning process. You learn to find what works and what doesn't with your kitty as ECID (every cat is different). You'll get there.

Just remember to have a lot of patience.