The location of the pain along with the signs and symptoms you feel during are classic cluster signs. Yes they can change in timing, length, frequency, go from episodic to chronic or vice versa, as several say here, the moment you think you know your cluster, it changes.
O2 is a go to suggestion, 15-25 litre per minute in a good non-rebreather mask. 100% oxygen. If your dr knows what clusters are you are ahead of the game, so few do.
I would get the other tests, as a precaution. Topamax aka topiramate has some unpleasant side effects, and is not always the first go-to drug.
Generally any abortive meds, such as triptans and such for clusters are rarely used orally, since it takes a while to work, nasal triptans or injections work far faster, but triptans can cause rebounds if over-used. If advil is working for you, you are very lucky most pain meds up to and including opiates and such tend to do nothing for a cluster.
I would go through the diagnostic criteria with your neuro, get the tests to rule out other causes and maybe ask/talk about a prednisone taper, verapamil combo before going with the Topamax. Others will have more suggestions and ideas, you may also want to have a look/search for the vitamin d3 regimen here, many have had great success with it.