In general, I would say that if you think of your family that way that I feel like family ought to be thought of, the answer is an absolute, definite yes, they should be told. Maybe if you really aren't close to them at all you might not tell them, but the impression that I have from what you've written is that, at a minimum, you want to be close to them, and I think that's enough that they should be told.
How to tell them is a really hard one. In my case, I'm very close to my family. I actually discussed the possibility with my parents on the phone a few days after the possibility came up that I might have ASD. It was really hard to say the words, but their response was basically that they weren't surprised. The psychologist wanted to interview them during the diagnostic process, which wasn't a problem because they already knew it was a possibility.
My brother, with whom I have always been close, was a more difficult matter, and I basically took the easy way out by giving my parents permission to tell him.
In fact, maybe that might actually be an easier thing for you too. You mentioned that you have several siblings, and the impression that I'm getting from your post is that they are closer to each other than to you.
Are you closer to one of your siblings that the others? Might it be easier on you if you told just one of them and asked that one to tell the others? Do you think that would be fair to them?
One thing: when I did tell my parents, I was basically telling them from a perspective of me seeking their council - not trying to explain my behaviour. I'm a bit concerned that if you come at it from a perspective of trying to explain your behaviour, they might interpret it as you trying to make excuses (even if they are valid excuses).
Hopefully your siblings will draw these conclusions on their own, but I wouldn't, at least at first, try to draw a direct link between your past behaviour and your diagnosis.
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Level 1 Autism Spectrum Disorder / Asperger's Syndrome.