You should get it in writing. You are diagnosed, but if you need to prove it to anyone, it needs to be in writing.
Trust me, I had a problem with this once. A psychiatrist did a bunch of stuff and told my mother I was autistic. (I was unaware of this.)
Then he waited awhile and finally wrote on paper that I had PDD-NOS. I understand why he did it at the time: I had an awful insurance company that would have either refused to give services at all because autistic people are hopeless, or institutionalize me indefinitely because autistic people are hopeless. (They tried to do this anyway.)
But, these days, if I tell people I was diagnosed with autism back then, but they see the diagnosis of PDD-NOS, they go "Oh that's not autism." Then they claim that I was only diagnosed with autism later on when it was safe to change the diagnosis to autistic disorder.
(I do happen to think that PDD-NOS is a way to say autism without saying it most of the time. But a lot of people think otherwise.)
So, when it comes to other people, you'll need the diagnosis to be on paper before they believe you. Oral diagnoses might as well not exist even though they're just as real when stated with certainty. And even if you don't need it on paper right now, you might need it later. Additionally, I did not need another paid session with my psychiatrist when I needed to have a copy of a paper diagnosis. I would just call him and then have him fax it to a fax machine. (I didn't have one, but I would go somewhere that had one.) He didn't charge for this.
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"In my world it's a place of patterns and feel. In my world it's a haven for what is real. It's my world, nobody can steal it, but people like me, we live in the shadows." -Donna Williams