Ultimately the diagnosis for non-24 involves a sleep journal, or an actigraphy sensor. However, that's only after checking for other causes that may only appear like non-24. These causes can include drinking caffeinated drinks at night, or staring into brightly lit screens at night, just as a few common examples. If you want to eliminate some things yourself, there are some behaviors you could change to see if it helps get you to bed at a regular time.
As a collection, the set of behaviors are referred to as sleep hygiene. WebMD has a good list for sleep hygiene (which is what I linked), however, it might be a good idea to compare it with the suggested behaviors other medical or psychological sites may have. I know many other websites suggest that if you're not falling asleep, you should move out of the bedroom and not return to bed until you're ready for sleep (...or sex). I'm not seeing that suggestion on WebMD, so really, compare lists.
Sleep hygiene eliminates many things that could make it look like you have non-24 (or Delayed Sleep-Phase Syndrome), while not actually having non-24. In the spirit of being thorough, it's a good starting point.
Non-24 is rare, especially in sighted people. Anyone who suspects they have non-24 should keep in mind that there is a very distinct possibility it only seems like they have non-24. Because of this, doctors that are well researched and thorough will most likely be testing for many things before arriving at non-24 as a diagnosis. It's pretty standard to test for sleep apnea, and poor sleeping behaviors. Sometimes they'll check for drug abuse, or request a psychological evaluation. Rarely there are a few other tests as well. Bad doctors often won't bother with testing during diagnosis, and will instead start slinging habit forming drugs that only work for a short period of time.
If you really do have non-24 and want to treat it yourself, there are options. There are treatments for non-24 that do not require any prescription drugs (at least in countries were melatonin is a non-prescription drug). They work for some, but they seem to be in the minority. I detailed the treatment I follow here. Most non-prescription treatments look similar, however, the treatment I follow is more involved than most.
My own personal opinion after reading your post is that it does sound like you have non-24. However, since this is a non-24 subreddit, that's a really easy assumption to slip into.