This is what Therians and Otherkin call a phantom shift and it is purely psychological (unless your belief adds that it is also spiritual). As mentioned before, it is not a physical shift. I'd also be weary of calling it a "spirit animal" as that is a culture specific term and most probably not one that you're involved with.
Therians and Otherkin often hold the belief that you don't "turn into" a Therian or Otherkin, but that you always are one and when you realize it, you "awaken" to your natural "form". Therian is specifically physical animals that do or have existed while Otherkin can extend to mental and spiritual beings/concepts for their "forms". Just like in the Occult community, there are fluffs who believe that there is physical shifting; however, that is not a representative belief of the whole group (also note that spiritual and psychological aspects apply to both Therian and Otherkin belief).
Phantom shifts are but one aspect of Therian and Otherkin traits. Others can be behaviors, mannerisms, or anything of the sort. Generally you'll feel as if you are psychologically or spiritually not entirely human, but you wouldn't do things like growl or bark or do something else of the like. People who actively try to be an animal (not saying you are or aren't as I don't know you) are simply wishing they were an animal and typically aren't actually Therian or Otherkin. Those kinds of people think of it as something "cool" when in reality is an aspect of who you are that you won't be able to dismiss; much like having eyes and arms. You may or may not like them, but it is intrinsically you.
Whether or not you are Therian or Otherkin is not for us to decide, but for you to find out. You may find that this is not the case at all with you and it's really a matter of self exploration and understanding.