It's hard to cut carbs in my household as it's full of tempting carbs and junk food, no veg at all apart from potatoes.
I appreciate that trying to follow a different dietary regime in a family is going to be difficult, are you the only one that's diabetic. You say you try to keep your carbs to about 200gms but that's about 800 calories which sounds pretty close to 1/3 of 2400 cals or about what somebody of about 20 stone requires to MAINTAIN weight.
You have two choices and it's entirely up to you, we can offer our thoughts but we can't tell you what to do. If your present regime with the amount of insulin you take and the amount of meds you take means that you regularly have BG in the 30s or 20s or even the teens, then something has to change before nature takes over and you must know what diabetic complications means.
Reducing your carbs to a much lower level than 200 gms is going to help you a lot, I don't think there's any alternative. As an example I cut out spuds, pasta, rice and bread (so that includes strudel) and my carb intake was about 40gms. I did that despite my wife being able to eat anything and eat like a horse and not gain weight. We're different, I get it, I have to behave different otherwise I will be heading towards an early grave and at 64, that's not so far off.
You are young and should have a good life ahead of you, not if you don't change your ways. As I said you have two choices, it's entirely up to you.
BTW, your sister
might be right about the diet coke. You don't have to believe me, or your sister, there's enough information available to study the effects of diet sodas, especially for diabetics. Don't forget, you asked for help, forum members want to help, it will seem hard to make drastic changes, but if it were me it's a no brainer, don't become a victim, take charge and sort yourself out. I'm sure your parents don't want a son who is ill all the time and trust me on this, no parent wants to lose a son or daughter.