I don’t personally know of anyone who has had anything similar that turned out not to be PsA, but of course most people I know with those sorts of symptoms are here on this site - there will be possibilities out there. Of the more common that I’m aware of, possibilities could include non-erosive arthropy associated with IBD (but then you’d need to have IBD and I think you’d notice), non-erosive arthropy associated with Coeliacs (it’s possible not to notice Coeliacs, but not likely), sudden onset polyarticular OA (yes, this is a thing, but I’ve never seen it reported to include the spine and I think your other post mentions that - it also tends to show changes on scans pretty quick I think), and less commonly I imagine there are other connective tissue diseases that might show a similar pattern if they are mild (though I understand most of them will have some sort of blood marker that your doc has likely tested for).
I had the guinea pig approach (for my possible atypical IBD, not PsA), where they put me on a drug that should resolve it (changed from Enbrel, which was great for my arthritis, but not my gut, to Humira, which does both), and figured that it was probably IBD if it worked. It did.
In your case, it is good to see your Rheumy being proactive, and I’d say that if after another 3 shots or so of Enbrel you are seeing substantial relief, the chances are pretty high it is at least an SPA, if not PsA. If it doesn’t work well, it still isn’t excluded (not everyone responds to Enbrel).
Initially I found the uncertainty of not knowing what it was (prognosis, disease control - all uncertain) really difficult, but after a while I realised that SPA and PsA are usually treated so similarly (in that the same meds, exercise, processes are used, but tailored to the individual), so stopped being hung up on what mine was, and worked within the framework to try to figure out what worked for me.
My Rheumy won’t diagnose PsA unless he sees dactylitis (regardless of CASPAR). I thought this was sheer bloody-mindedness, and was very frustrated about it initially, until I saw the comparable approval processes for the Biologics on PsA versus sero-negative RA (which is the box our government puts SPA in). Glad the formal diagnosis for me is still sero-negative RA, that man knows how to work systems - much better approval processes and many more medications available. I fit CASPAR and am happy that I belong to this community, even if I don’t fit the labels well (they couldn’t find one that fit for the IBD either…
).
I understand how frustrating it can be not knowing. We are all unique though (nowdays I just think of myself as ‘special’ 
), and regardless of what it is, you will still need to go through the trial and error of finding out what works for you (exercise, rest, alternating the two? pacing? ice, heat, arthritis sprays? biologics, traditional dmards, NSAIDS? meditation, laughter, family time, sleep?) Those are the things you can control, and they are well worth your attention 