You are not a bother at all! I do this a lot :D
I can understand why you’d freak out, especially if you’ve only recently had the diagnosis yourself, and your parents haven’t taken it well. DID (for my other readers, Dissociative Identity Disorder) is one of those big scary “cinematic” diagnoses that tends to make people interrogate because it’s semi-rare and usually the product of trauma, which especially makes parents wig out because it means they didn’t protect you when they think they should have.
It’s good that you want to talk to them about their reaction to the news, and I hope you understand that it is the news they were reacting to, not you – while they may have trouble separating your diagnosis from your person, if they’ve got you in treatment and want to be a part of it then I think they probably do genuinely come from a place of “love you and trying to help”, they’re just being super bad at expressing that right now. Which doesn’t excuse what they did, but it may help you understand why they did it, which can take some of the sting out.
I mean, I think what you suggest is good – make a few notes to yourself about the things you want to say, like have three main points you want to make, and stick to those points when you talk to them. “The way you reacted really freaked me out”, or “I need to talk about why you didn’t believe me” or “I really need you to trust me and help me out, I’m scared too” or whatever it is you feel you need to say. Possibly it would be best to do this out in public where their emotional reactions are likely to be dampened, but that can be harder on you, so you know – pick your venue with care.
You may want to consider having your counselor or doctor or therapist talk to them too. You’re not alone in this, someone diagnosed you – why not have them handle the flak from your parents? After all, if you need to get parental consent, surely the doctors are going to need to get your folks to sign something at some point. If your parents are freaked out, an expert with a degree can explain the technical (not the personal) a lot better than you can, and won’t be as hurt when your parents ask a lot of dubious questions about it.
But also – you’re old enough that the person or people treating you talked to you about it instead of going straight to your parents, and you’re old enough to be pretty coherent about what happened, so….do you need their permission to change your treatment? I honestly don’t know much about DID but I was given to understand that a great deal of the treatment for it is focused around treating the initial trauma(s), like, it’s not like you’re probably going to need surgery for this. How much parental consent do you need? Teenagers in particular tend to forget that they don’t need parental permission for everything they do, because they have for so long. Can you change your treatment plan without needing their permission? If so, I say go ahead and do it, as long as your folks aren’t gonna actively cut off support you need.
So, I think it’s great you want to talk to your parents and I hope they come to understand the things you’re dealing with – but remember that your framework as a young person is shifting, and you may be able to do what you need to do for you regardless of what they think you do or don’t have as a diagnosis.
Good luck. It’s a scary thing to face, but more knowledge is always better than less. :)