J.S.
I am ADHD as is my ex. All four of our kids are ADHD and like my ex one is autistic. So what, just labels to understand the behavior. My older two were straight A students, best kids in the class, all from just a small does of stimulant medication. My third, with spectrum, sounds a lot worse than what you are describing and even he is doing great now. My fourth is just well, a lot like me.
My third had an awful preschool teacher. She was, well she wasn't very nice. She tried to diagnose all the kids as autistic. Kind of like all you have is a hammer every problem is a nail. He did turn out to be autistic but that lady, urgh! She kept saying it was clear because he touched every book, didn't make eye contact, basically symptoms that are also symptoms of ADHD, things I did. I guess what I am saying is find a good psychiatrist and listen to them. They are the only people I know who can weed through what is and what isn't.