I'm telling you that, diagnosis or no diagnosis, I raised two extremely challenging children. I was chronically short of sleep the first seven years of my oldest child's life and I was a full-time homemaker. I didn't also have a paid job.
I'm quite familiar with how crazy making special-needs kids can be. I didn't need a formal diagnosis because I was homeschooling, so I didn't need to justify getting accommodation. I was their teacher. I could decide to just accommodate them, without an IEP.
Some things they did get formally identified:
Gifted
Dysgraphia (in the IEP when they were in school)
A serious medical condition
Eyesight issues
ADHD was ruled out for my oldest.
Probably other things I'm not recalling. It's been a lot of years.
Things I learned about because they seemed relevant to our needs, though I had no official diagnosis:
ASD
Dyscalculia
Face blindness
Sensory issues of various sorts
My younger son, the one I found easy to deal with, was one of the kids that qualified his small kindergarten class for additional part-time help. Another student had a formal diagnosis of ADHD or similar. Another was in a wheelchair, having lost both legs to a serious and life threatening infection when he was younger.
I would visit his class and it was obvious he wasn't like the other kids. He was the only child in the room who couldn't keep his butt in his desk chair.
I hadn't noticed what a hyper and aggravating mess he was until I saw him in a classroom of other five year olds because, at home, he was the (relatively) quiet child that didn't drive me batty.
I don't need a formal diagnosis to say "Yes, I dealt with a child doing things like that all day, every day, like you described."
I also took classes and what not. Dealing with my crazy making children was my full-time job for a lot of years. I took it seriously and did a lot of reading and took classes, etc.