Some people eat no carbs, some eat low carbs, other eat a relatively normal diet, carb wise, but I have to admit, you ar the first diwbetic I have ever met who drinks energy drinks. I associate them with feeling awful, because they are a "hypocure" for me.
You don't say what you BG control is like? I used to be like you, and could eat and not put on weight...but this was becasue my Bg was so high, i wasn't able to put on weight.
If you BG is good, and you don't put on weight..then I admit to jealousy, but if you BG control is not good, please don't be as daft as I was, and sort yourself out before you get complications.