LADA is Latent Autoimmune Diabetes in Adults. Many people think that it is just Type 1. More and more people have been diagnosed as LADA/T1 over the last 10-15 years as the tests for antibodies have become more available. You have been diagnosed very early and should consider yourself kinda lucky as you have some opportunity to affect the progression.
LADA/T1 is typically a slow moving form of T1 where your condition degrades over time as you lose more and more insulin production. I have seen studies which suggest that you can go for years before needing insulin. One key thing which seems to help is keeping your blood sugar at normal levels. If your blood sugar gets high it can start to poison your pancreas accelerating the decline in insulin production.
LADA/T1 can be a confusing condition. Some argue that you should move quickly to using insulin and treating the condition as T1. But if you don't need supplemental insulin as in your case adding insulin can be counterproductive. And T2 medications actually do help. One authority (Stanley Schwarz) likens LADA/T1 to be more of a fast moving T2 than a slow moving T1.
In either case, you need not fear insulin. Insulin is just another medication. I've been on insulin for more than six years and I have to tell you injecting insulin hurts less than checking your blood sugars. And it just becomes routine. Part of dealing with your fear can be to simply talk about it. What about insulin scares you? Is it the injecting part? The possibility of hypoglycemia? Is it the final conclusive demonstration that you do in fact have diabetes and will always have diabetes?