For a long time, I felt like this too. It was like I just knew that I had a "real" fursona, somewhere, but I had no idea what species it was. I kind of wished that someone who knew me would pick what they thought fit me best, just so I could see what it was.
The irony is that I had already written a furry character, in a long series of stories. One that I identified with so strongly that I regularly hugged a plushie of his species for reassurance. He was an arctic peregrine falcon, and I'd been through a lot as him. Maybe he was so familiar that I thought he was boring. And yet, I kept writing as him.
At some point I decided that it'd be better to be a generic bird of some kind, than a raptor. I didn't see myself as a predator, and I didn't like to eat meat, either. Later on while I was in a store I saw a tree swallow plushie, and it was so striking that I just couldn't stop staring at it. While trying to act like I wasn't interested. In the end I decided to use the character I already had, and just change his species.
I don't think most people exactly have this kind of thing fall out of the sky and hit them on the head, and even for me it wouldn't have happened if I hadn't already been looking.