We can help you! As others have said, home testing is the best way to know exactly what is going on with your kitty. Please consider learning to home test. Once you know how the insulin is working with your cat, you can make adjustments to correct her BG levels and help her get better. It is doable, and much easier (and cheaper!) if you learn to home test. Diabetes is very manageable in cats, all you need is the right tools and knowledge, and we can help you with that.
You will need a human glucometer and test strips for it, I use a Relion Confirm (Walmart's brand). It works great, and the test strips are very inexpensive. There are many choices, the most important thing to consider when buying a meter is the cost of the test strips because that will be your biggest hometesting expense. Try to get a meter that requires a small amount of blood (0.3 microliters is the smallest) because that makes it easier to get tests done without wasting strips. You will also need lancets (to poke her ear to get the blood), you can either use them freehand or use a lancet pen. There are videos that show how to do the testing, it isn't that hard to do once you get the hang of it. You will want to use treats to reward your cat after testing, even if the test is unsuccessful. You will be surprised how quickly it becomes part of your routine!
When you go to get the meter, you should also pick up some ketostix. They are used to test the urine for the presence of ketones. It is important to do that, ketones can make a cat very sick, and it is much easier and cheaper to treat if you catch it early. They should be available at any pharmacy.
If you need someone to help you learn how to home test, there may be someone in your area that can come and teach you. Let us know if you want help, and we will try to locate a member who can help you.
She is hungry and losing weight because she is not regulated. Because the insulin is not working for her, she is unable to use the food to fuel her body, so she is trying to eat more to compensate. It's fine to feed her as much as she will eat. There is a lot of information about what sort of diet to feed diabetic cats here, you should read about it but don't change her diet just yet. You should learn to home test first so you can adjust her insulin if necessary.