Two things work well for me: stimming and spending time doing a quiet activity that I love.
Stimming helps in the moment, even intentional stimming. (If you aren't aware, stimming is a repetitive activity, sometimes involuntary or unintentional, that provides stimulation of some type that is pleasing. Common stim include biting/chewing things, playing with items/fidgeting with things, flapping hands or fingers, rocking or moving. For me, I bought a silicone necklace that is chewable but also just looks like jewelry (search 'Zen rocks' on Amazon). Chewing when I'm anxious or nervous helps me tremendously. It sort of feels like if you imagine that anxiety is a rising pool of water that eventually overflows into a meltdown; stimming is like opening a gate in the dam that lets the anxiety out and slowly allows the water levels to drop.
The other bug thing for me is to do something I like in a quiet, controlled environment. My thing is watching very familiar sitcoms that I love. When I'm really bad with anxiety, this is one of the only things that helps me. I turn the volume down to a comfortable level, and I can focus on the show and not my thoughts.
Another thought I had is that he is going to need to understand that ASD is a disability, even if he doesn't feel disabled or doesn't think he needs special considerations. There are things he can do to help himself, but he needs to realize that he isn't like other people and can't be exactly like other people.
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You don't need to hide, my friend, for I am just like you.