My cat Asterix has diabetes. It sounds a lot worse than it is. It's just like diabetes in people. It's a big pain in the butt because you can't just go away for the weekend with a big bowl of dry food on the floor, but your cat will probably not die of it.
The worst problem with a newly diabetic cat is getting them to eat right. Once you have that licked, your cat may not even need shots any more! (But most cats don't mind shots. It is much easier to give a cat a shot than it is to give them pills or even liquid medicine. They hate blood draws, but insulin goes just under the skin and they barely feel it. Asterix will come to me and beg for one if he feels bad because he knows it makes him feel better. Asterix is diet controlled now, but if he gets into something he shouldn't--he's mischievous and smart--he will have to have a shot.)
Diabetic cats do best on an ALL WET FOOD DIET. (So do most cats, to be honest. Dry food has too many carbs and not enough water.) Cats love dry food because of the taste enhancers they put on it and it can be hard to break the habit. Asterix didn't mind the switch, but I also had to switch my other cat because he lets Asterix eat his food, and that was a trial. As you know already, cats need to eat every day or they have liver problems, so you may have to switch them over gradually.
Generally speaking, you want a canned cat food with less than 10% carbs. That means it doesn't have "gravy" -- just a pate. My boys do well on relatively cheap food--the "meat by-products" are often the organs and other parts of an animal that a wild cat would eat, but humans most often won't consider to be meat.
Cat Info.Org canned foods
The Feline Diabetes Message Board and CatInfo,org are life savers.
Talk to your vet. Let them know you are willing to change your cat's food and ask if they want you to do home testing. If your cat's case is challenging you may want to do home testing too (whether your vet is enthusiastic or not). Asterix was an easy case so I just keep an eye on him.
You can find cat sitters who know how to give shots, so you're not stuck at home for the rest of your cat's life--it's just expensive.
There will be people who have never had a diabetic pet who will encourage you to put him down. They're full of s**t. All you need to keep your cat alive and happy is the right food, insulin shots and a little extra attention & love. Feel free to friend me. I have a job so I'm not on during the week except in the evenings, even though my home computer is on so it might look like I am. But it should be OK.