Possibly autistic adult?

Since discussing my 4 years old possible having autism with the sen teachers at her pre school and seeing how she is and how she acts I’m starting to think about me, and how i used to act when I was younger and how I still act now. When I was younger people just shrugged it off as me being super shy and nervous, I struggled meeting new people, I’d get shy and sit in my bedroom when my own family was round my house, I struggled going to school and only now am I realised maybe it’s not just me being shy, or nervous just maybe my parents didn’t know about autism when I was younger and didn’t see the signs. I still to this day struggled to talk to people, Meet new people I get really nervous and anxious talking on the phone I can’t do it I have to get my partner to do it, there’s so many things my daughter is doing that I do actually do myself, she is being assessed in January, how easy is it for an adult to receive an autism diagnosis and what it the process? I struggle to get any doctors appointments to discuss this with a doctor so I really don’t know what to do.