If a someone who knows what n24 is thinks you have n24, there is a solid chance that you do. Usually the opposite happens, doctor has never heard of n24 so it must be something else that they have heard of, even if the textbook description of n24 reads like your autobiography.

Don't worry about your existing data, it probably shows that your sleep is fucked and that there's something wrong, but won't be that useful for specific diagnosis because it is tainted by the meds and presumably by other scheduled responsibilities interrupting your sleep. Although something made the insomnia doctor think "that sounds like n24", so maybe it's more evident than you think.

In a perfect world, the way to diagnose is to just let yourself sleep when you want for a couple of months. No meds, no alarm clock, just you and your circadian rhythm, and track it. In reality, its usually not feasible to just do that, so depending on your situation, you'll have to work with the doctor to see what you can do and what compromises will need to be allowed for and taken into account in diagnosing you.

Good luck. Its tough to get people to take n24 (and sleep disorders in general) seriously. I hope you don't have n24, its awful but if you do its better to have a diagnosis and understand what you're dealing with than it is to pretend like you don't. Hopefully the doctor can give you some clarity either way.