I find that it helps not to look at things in such a binary fashion, or to cling so tight to notions of truth. One part, or facet of who you are is unwell. The idea that you are faking it is a very familiar one to me, but if you imagine having a broken leg, that is real. That your other leg is fine does not negate the illness. Same with you brain. The problem is that the illness you have distorts reality by its nature, include the reality of itself. Do NOT think too much about that, it will get dangerously recursive.

tl/dr don't be hard on yourself, yes it's real, maybe go see your pdoc.