I was also diagnosed as a T1 as a young adult, age 30. I am probably LADA as well but back in 1984 they didn't do antibody tests to confirm.
You received lots of good advice here. Eating too many carbs is trouble for many T1's. The medical establishment and dietitians are so indoctrinated with fear of dietary fat that they reflexively, almost without question, push a high carb low fat diet.
After 28 years with T1, I finally tried a low carb approach (about 50-70 grams per day). I dropped 20 pounds, took only half as much insulin, and my number of hypos went from two or three per day to two or three per week. In addition, my overall control and A1c dropped. Bernstein's law of small numbers means that taking lower doses of insulin leads smaller mistakes.
Counting carbs and dosing accordingly is a good practice. Unfortunately, your body's sensitivity can fluctuate day to day and from morning to night. Even very accurate carb counting, using a scale, will still produce out of range BG's. So, the less insulin you take will mean milder lows and highs.
Congratulations for your aggressive curiosity about diabetes. Even back in 1984 the doctors told me that they noticed that education and knowledge about diabetes made a big difference in the long-term outcomes.
And yes, insulin can make you fat! You are smart to keep an eye on the number of carbs, the amount of insulin, and the trend of your weight.
I'm sorry you got this diagnosis but you seem to be a smart and practical young woman. Good luck to you!