Meh, nearly a necro thread, but I thought I would add my experiences as well.
I feel crazy whenever this happens. I know I am physically human. No question that I find a visual shift impossible. But still, the mind is a powerful thing. So, I have two fursonas representing two parts of me. One, Glitch, is my typical me. Quixotic, imaginative, and usually let down all to often because of these traits. I am usually her in my dreams.
But Axis, the one representing my rage, is the one that is most commonly shifted to. Like many, when I get extremely angered, I begin to shake and tremble. Past that point, I feel Axis' mane rising up on my spine, a phantom tail brisling, ears pressing downward, and sometimes the burn of scars on my extended canine muzzle. Claws are a very common thing for me to feel. Sounds like something that belongs in dreams and not real life.
I attribute all of the above to a very active imagination of mine. I'm not batshit insane; none of us are, really. We just have a better sense of who and what we can be in our minds. Quite frankly, being human-bodied is.. tolerable.. but human-minded? No, not for me.