Did you complete any forms before the assessment? I had to complete a few forms before assessment which asked me questions based on the diagnostic criteria which then went towards the psychiatrist's final evaluation. Assessment styles seem to vary wildly between services and counties, though.
To answer your question more directly, though, yes, I thought of loads of things I forgot to mention in assessment afterwards. But then I was given my diagnosis at the end of the assessment so it sounds like your psychiatrist deals with things differently, at least in that example.
If I can give you some advice, I'd suggest you put it out of your mind for now until you get the result and if you do not agree with the result, appeal with the extra information (if you can). It would be a good idea to start a log of supporting information when you remember it, as well. Keep it somewhere handy, like a small notebook you keep on your pocket or a notes app on your phone. I think that's good advice for everyone going into an assessment.