What has happened to you happens to lots of non-diabetics too. It seems hormones have a lot to do with it. Doing a keto diet is certainly worth a try. I simply removed all carbohydrate from my meals. If you do this, be sure to adjust insulin dosages accordingly. Basal may also have to come down as the body uses more fat for energy.
For breakfast I have an egg dish made in the microwave - 3 eggs and 50 grams of cheese, to which I add some combination of mushroom, onion, broccoli and cauliflower. Only the onion has some carb in it. For lunch I have a chicken, tuna or salmon salad, at this time of year with avocado. Also add some combination of capsicum, tomato, cucumber and riced broccoli/cauliflower. For supper I have a portion of frozen protein food, done in the slow cooker and stored in portion sized containers, together with cooked vegetables.
For me the biggest challenge is avoiding use of carbo to treat low blood glucose. It can take a while for insulin doses to be adjusted suitably and unexpected exercise, stress or eating out messes up the process. Eating carbohydrate stops ketosis, which is required for fat to be used for energy. This may stall weight loss, but don't let it get you down. Also be aware that it can take months of being in ketosis to become fully fat adapted. Retraining the metabolism is not an easy process.