I'm on meds that increase my apetite, so I can relate a bit, but I suffer with anorexia and the meds were intentionally supposed to increase my apetite, so in a way I can accept it more. I still know how you feel though, you can feel out of control because even though you're sure you've eaten enough, you still feel hungry and if you allow yourself to eat you then feel bad and greedy.

I think exercise would be great for you, it would help with your fitness levels and also boost your mood. I know it's soo hard to feel motivated when you feel so low, but I think that will come. You could find something that you perhaps enjoy instead of actually working out in a gym or something. Do you like walking? I find that's a really easy one and it can be so enjoyable and calming if you can perhaps go somewhere nice, a bit quiet, out in the countryside...?
Do you have any friends or family who could perhaps do something with you?

What's the diabetic diet like? I think it's important to not deprive yourself of everything enjoyable, it has to be something you will stick to and not be hating every moment of it. .
What sort of things do you crave when you have cravings? If they're 'bad' foods you could perhaps find some healthier alternatives, so when you feel hungry you're still eating but it's better for you.

Anyway, good luck. x