Only caveat about this is that if you truly distance it from what you call "me", then it can become something you are fighting against, and that is seriously unhelpful. My thought is that it is you in that it is something in your body and your body is not separable from your mind. It is all "you".
There is definite value, however, in making sure you do not identify as a PersonWithFibro, or allow that one thing to define you in a major way. That also will lead down a negative path.
As with everything else in life and especially with fibro, balance is required for optimal health.
What works for me is thinking of it this way: I am a person who has fibro. I am a person who has chronic depression and pain. Etc. That way the phrase "I am a person" comes first. I am not the pain, I am not the depression or the fibro, nor do those things have me. This allows it to be perceived by myself and by others as only a part of me, like having a certain eye color, or being tall or short or whatever gender. Definitely there, not something that can be separated from self but at the same time is not by any means all of or a definition of who a person is.