Well, pretty much. I wrote down my symptoms as they happened. I just observed my symptoms in a two-week span as they occurred, and wrote it down (sort of like a dietician would if they wanted to observe if you perhaps have a food allergy, or the reason why your cholesterol is high, etc.)
For example, I wrote down my hallucinations as they happened. If the voices are really prevalent I write down the details. If you can, write down a few specific, recurring details. I'm not exactly sure of all the things you're dealing with; if it's a problem with your mood, write down moods that keep recurring and how they are causing you problems. If it's a different issue, write down a list of what it is, give a general description of it, and give them information on how it's negatively impacting your life. Those are the kinds of things that they would be looking at.
Also, if there are specific reasons as to why this information didn't come about earlier- for instance, if you were to embarrassed to share that when you started, if the problem wasn't that bad when you started therapy but now it's a problem, or if the issue only appeared after you'd been in therapy a while- try to explain this (either at the start of the list, at the end of the list, or out loud- whichever you feel more comfortable doing.
Then, when you feel you have a complete list, you can either hand it to your therapist and tell her/him something like "I think these are important details, and may affect my diagnosis." or "These are some things that have been bothering me, and I don't think that my diagnosis is accurate."- just something that you feel comfortable saying that you think is going to be understood. If you have a really good relationship with your therapist, you can just hand her/him the list and ask them to read it and see if it changes your diagnosis. It all depends on what the additional symptoms/details are and what you're more comfortable doing. If you can remember the info without a list, then you can present it orally. If you would rather write out a list and then present it orally, then that might work as well.

(p.s.- What I did was, when my therapist contacted me to check in on me, I told her that I had something to share with her during the next session. I gave her a really long list, and I explained what the list was in the introduction.)

Good luck! Hope this helped a little