Hi Carolyn!! Here is a link to an outstanding article by veterinarian, and feline diabetes expert, Dr. Lisa Pierson. It explains everything you need to know about feeding a diabetic cat:
http://www.catinfo.org/?link=felinediabetes
The basics are to feed an all wet diet consisting of no more than 10% carbohydrates and eliminate the dry food altogether. SOME Fancy Feast varieties qualify as less than 10% (the classic varieties) while others do not (the gravy varieties). There are many other brands to choose from, though Dr. Pierson does not recommend the "prescription" foods (she says they are expensive and of low quality - that they do not contain any magic ingredients to help with diabetes - and are often higher in carbohydrate than the recommended 10% or less.
When you switch to an all wet diet, your cat's BG numbers WILL drop, possibly dramatically, and may require a decrease to his his insulin immediately. Here is an excerpt from Dr. Pierson's article, though I would encourage you to read it in its entirety as well.
-------
"Many cats that are in a diabetic state no longer need any insulin when they are finally fed an appropriate low-carbohydrate diet. Others will always need some insulin but the amount necessary to maintain proper blood glucose levels is nearly always significantly reduced once the patient is on a low carbohydrate diet.
Please re-read the previous two paragraphs carefully. If you change your diabetic cat's diet to one with lower carbohydrates, he will, in all probability, IMMEDIATELY (not days or weeks later) require a reduction in his insulin dosage. He may also immediately go into 'remission' and not need any insulin at all. If this warning is ignored, you may very well end up with a cat in a hypoglycemic crisis (dangerously low blood sugar) which can result in death, or brain damage.
If you take only one point away from this page, it needs to be the understanding that if you stop pouring carbs into your cat by switching to a low-carb canned food diet (or even a dry food diet with lower carbs than you have been feeding), you MUST be aware of the probable immediate and significant impact on your cat's insulin needs."
--------------
Related to your cat being hungry all the time, the experts can probably better speak to this (I am still relatively new), but I have seen many posts here recommending that you make food available to the cat throughout the day. Some people feed 4 times a day, while others just leave out food all the time. They say that diabetic cats tend to be hungrier than others. Again, though, the recommendation is that you feed them only low carb wet food and snacks throughout the day (no dry). Maybe with the elimination of the dry snacks and feeding more frequently, the BG numbers will even out more. Others, please weigh in.
Best of luck to you!!
Melanie