Hallucinations When Tired

I noticed two things that happen when I'm very tired, both of which seem to be abnormal (compared to people I know). They could both be seen as hallucinations, depending on your definition.

1. Visual Hallucinations:
My vision gets very slight hallucinations. Nothing huge, mostly I'll just see something move in the corner of my eye and when I look I'm sure nothing moved. It is not as spooky as it sounds, just odd. And like things just change ever so slightly. For example I was on a bus and staring at the ceiling which has a pattern of holes punched in it. I was spacing out when the holes started to get spiky and not circular. As soon as I focused they returned to normal. I do actually see these things however; they are not just my imagination.
2. Mental Hallucinations:
These happen to me when I'm dreaming all the time. It is basically just a logical error. Like I'd see a super tall tower in my dream and think it is "10 feet tall". I still would understand how tall it is, but for some reason I would still say/think it is 10 feet. When I'm tired, these carry on into real life but not nearly as potent. The strongest examples are when I'm dealing with the least physically tangible things, such as math. My subconscious appears to personify numbers. Like when I multiply 5 and 8 I might mentally perceive them smashing into each other. It is a passive thought, I can choose to ignore it, and it certainly has no effect on my perception of reality, but it is definitely there. Also when I am really tired, these things become more powerful, sometimes to the point where they can confuse me and lower my score on tests.

My brother also has the visual hallucinations exactly the same as me, but not the latter part. Any thoughts on what this could be?

And for the second example when I say the logical errors get more potent, the worst it has ever gotten (after 2 weeks of very little sleep) was a time when entire stories involving the numbers were playing out in my head. Again, they don't actually affect my perception of reality or anything, but they do affect my mental performance because they eat up focus and attention.

Dream logic is dream logic. You often find yourself laughing at "jokes", that, when recalled, do not make a sliver of sense.

The hallucinations you describe are mild, and can be either optical illusions, or caused by being tired. I often see spiders or flies move in the corner of my eye when I'm sleep deprived. I think it might be my hair moving (?) and that being interpreted as something else. Or nothing at all being interpreted as something. Additionally, when I am close to passing out, patterns like that (laminated floors/wallpapers/whathaveyou that look like sand, polka dots, checker boards etc) start to move about. I remember asking if there were ants on the floor because I couldn't see that well, but saw something that looked like movement. I wasn't convinced though, looked closer, none the wiser, then passed out.

Do these things ever happen when you're well rested, well fed and happy? Because I suspect they don't, in which case you needn't worry.

Only a little bit when I'm not tired, and very occasionally. I just remember last winter when I was overtired most of the time and I lost touch with reality for a long time. Not like schizophrenia where you can't distinguish between real things and fake things, but I just wasn't sure what was real any more and it can get really scary.

What, derealization? Where you feel like you're watching yourself, you're far away and/or nothing feels "real"?

Yeah, take care of your sleep.