I'm going to go against the grain and say I would not worry in detail if or if not you are truly a therian, if or if not you fall into an other label. I think therian groups fall into a bad habit of trying to break the vast, inexplicable, spectrum of experience into neat clear cut boxes.
Being both transgender and a therian, I find the concepts of choice, innate being, voluntary, and involuntary identity brought up often and difficult to grapple with. And I think at the end of the day if someone chooses an identity it doesn't make that identity less valid. If my husband, for example, tells me tomorrow he's choosing to be a cat, then who am I to tell him no? To tell him his choice is pointless? To tell him that he can't do it like that? I think a lot of therians want to call it involuntary and innate because it seems more legitimate that way, "I'm not playing pretend this is just who I am".
But another reason I don't like this rhetoric is because, well, as an autistic person prone to self doubt and feeling like an imposter, it is really hard to know how to distinguish between something I choose versus something I am. In regards to being trans, I don't think there is anything I could do differently to change how I feel, but I Can choose How I interpret those feelings, how I act upon them. Is that count as a choice? Does it matter to the transphobes if I chose it or not? They already think I do and I don't want the only reason someone treats me like a man to be because they think I had no choice, that I was afflicted with ungracious malignancy. Re therianthropy, where there is even less open discussion and set social paths for people to follow who feel like or want to be an animal, it can be even harder to discern those feelings.
My biggest advice is to not rush into figuring it out, don't try to force labels. Don't try to nail it down right now. I've felt like a deer for a lot longer than I even knew about but when I had been worrying over figuring out the label (as I had months ago and years before that) I felt too scared to embrace a part of myself because it felt like I was just choosing it when in actuality I was just choosing to act on those feelings. Months later, after I stopped trying to figure it out perfectly, after I stopped trying to see it exactly, what I was became so clear.
Good luck