'In my mind it's real'? That doesn't make it real though. You were not an animal in a past life. Let me make that very clear. No scientific evidence has been found for anything close to reincarnation. The more research that is done on the brain, the more we understand a very simple truth: the brain as we see it, all on its own, is enough to explain human consciousness. All by itself. No soul. No past lives. None of it. None of it exists.
I don't believe you made it up. Someone, probably on Tumblr, had the idea before you. And even if they genuinely believed it, they still made it up, per say, because it's not real. This is not a matter you can debate. Until you can actually quantify it somehow, it isn't real, and I think that for the sake of education you should think of the other explanations for why you could identify so strongly with an animal.
And the other, more rational reasons are innumerable. This is what I don't understand about otherkin. There are so many better explanations that make so much more sense. And because you refuse those and go for "I'm a dragon" or whatever, I think less of your intelligence.
Sorry if that offends you, but to paraphrase Hitchens, if you say you're offended I'll ask what your point is.