Atheists believe in themselves?

[Angrboda]

I don't always even believe in myself or what's all around me. Sometimes things start feeling completely unreal and I have to stop and think. But I don't think that's normal or particularly healthy on my part.

I'm not a doctor or anything, but that doesn't sound the least bit abnormal or likely unhealthy. Similar types of experience (not just abstractly reasoning your way there) are pretty well within the range of normal. Some people have few such experiences, or very minor ones, some people have it a lot, or very intensely. It's simply an aspect of one or more of the mind's normal coping mechanisms poking its head out and saying, "here I am."

(ETA: As part of a whole group of symptoms, it might indicate the possibility of some sort of disorder or that you have some tendencies, but in and of itself, I don't think it means much.)
(ETA2: Some people who experience similar symptoms a lot carry something with a strong odor along with them, and when they feel themselves slipping away, take a whiff of it. Smell is one of the most powerful stimuli. There are other techniques.)
(ETA3: It also occurs to me that it could be job related. Derealization is not an uncommon reaction to social overload, having to deal with too many people, too much of the time, beyond that which is necessary to get one's emotional needs met.)