I learned about Asperger’s when I was 13; I wasn’t officially diagnosed until I was 20. (It took a lot of convincing to get my mom to realize it.) However, I had to see 3 psychologists to finally get the diagnosis.
The first ASD specialist I saw said she couldn’t actually diagnose me because she was an educational psychologist. She just basically said that it was possible I had ASD. It was a wasted hour, to be honest. My first actual assessment was typical of what a young child would receive (because the place I went to usually only assessed young children); it included an IQ test, the ADOS, a short interview with me, an interview with my mom (while I took the IQ test, I believe), and some anxiety/depression self-report forms. It was pretty much a disaster; the psychologist apparently didn’t ask my mother the kind of questions she should have asked and ultimately diagnosed me with social anxiety.
In hindsight, I learned that a “typical” assessment is not appropriate for an adolescent/young adult who suspects ASD, so I don’t think you should worry about how your assessment went. Like you, my motivation for an official diagnosis was school accommodations so I was pretty devastated. However, I ended up being diagnosed with ADHD about 4 months after that initial assessment (by a psychologist who said that I definitely had Asperger’s and that I should go see a local ASD specialist) and was able to get accommodations with that diagnosis.
I actually had the psychologist’s info for a while but finally decided to make an appointment with him after my ADHD diagnosis. So I went to see him and he diagnosed me with Asperger’s (ASD Level 1) about 20-30 minutes or so into a one-hour appointment. He mostly asked my mom questions, probably partly due to the fact that I couldn’t answer his initial question of why I was there to see him. According to my mom (because I didn’t notice this), he changed his approach after that and only asked me concrete questions like “How old are you?” I think the last 30 minutes or so was basically spent answering my mom’s questions (like why weren’t my ASD symptoms noticed earlier), discussing my future career plans and how he could help me work toward them (I want to be a child and adolescent psychiatrist who specializes in assessing teens and young adults with ASD), and my “special interest” (which, at the time, was the DSM).
That was 2 years ago. I now see him about once a month.