I know that feeling; much more than I'd like to admit. It swallows you whole and pretty soon, it becomes your identity. So much so that if somebody were to ask you who you were, you'd most likely respond with, "I'm *insert illness here*." You don't even identify with your own name anymore because your illness has become your identity. You're nothing more than a living, breathing embodiment of your illness. You forget who you are. The spaces inside you that once held your dreams, accomplishments, hobbies, no longer exist. You are a vast black hole of nothingness.
But that belief of yours is entirely false. You are so much more than just an illness. You are your personality, your hobbies, your dreams, your passions, your talents, your heart, your soul.
And yes; your illness is undoubtedly a part of you, one that may appear bigger at times, but it is not you.
You are no more your illness than you are your brain or your kidneys; because that would mean that your brain or kidneys are the only organs in your body when there are several others.
It cannot compare to the countless other things that make up you. It can't even come close.
There's a reason why you say you "have" an illness rather than you "are" an illness -- because it is not your entire being. It is not you.
You may have it, but you also have countless other things such as your likes, your dislikes, your best friends, your favorite songs, your generosity, your interests, the list could go on for miles.
We aren't just one aspect of our beings. Humans are not that simple. We aren't one of those one-dimensional figures we learn about in geometry, and wouldn't it be a shame if we became one.