I am sorry to hear about your diabetes issues. I am only a T2D and what I say should be treated only as a suggestion to be discussed with your doctor. It appears to me that you need to reduce the quantity of insulin you are taking and to do that you need to reduce your carbohydrate intake. It is important that this is monitored at all times so that any reduction in carbs is met with the appropriate reduction in insulin. You don't want to get to the point where your body thinks it is starving as that might risk ketoacidosis. You should therefore convert to eating a lot of vegetables, high level of fatty foods (butter, nuts, olive oil, eggs, etc.,) and meat for protein. Meat also contains fat and if your not vegetarian good for you. Fish and walnuts will also give you Omega 3.
Eating fatty foods will not make you fat. If you can reduce your carb and insulin intake, your liver will eventually break down your own fats into ketones, which it will use instead of glucose (sugars) to feed from. This is a very stable energy source for your body which does not fluctuate. You will then only require to use a small amount of insulin to deal with the modest carbs in your body and maintain a steady blood sugar reading within the normal range of 4 to 6 that non-diabetics enjoy. The reduction in insulin will reduce and possibly resolve your insulin resistance.
Because T1Ds manually maintain their insulin levels depending on the carbs they take it is sometimes too easy for them to eat what they want and as much carbs as they want believing that they can simply deal with the sugar in the blood through their insulin intake. It can be forgotten that T1Ds can also suffer from insulin resistance in the body caused by having high levels of insulin over a prolonged period of time in the blood. This high level of insulin will over time be detrimental to your body as it leads to other health issues including neuropathy, retinopathy, kidney and heart problems and has also been linked to Alzheimer's. As you have discovered the insulin resistance means that your organs and muscles are not taking up the sugars from your blood and this in turn sends signals to your brain asking for more sugar, despite the fact that you have eaten. You then have to inject more insulin which is simply poring more petrol on the fire.
Insulin resistance is what T2Ds have to deal with on a daily basis and you need to adopt some of our methods of dealing with that issue. Moving to a low carb high fat diet (or keto diet) will not reverse your T1D, but it will at least stabilise it and keep it at a more constant low level, which should make it easier for you to control. Remember because you are a T1D it is not as easy for you as it is for a T2D to go straight into this diet, and you should do it slowly and with consultation with your doctor.
I hope this helps and wishing you well.