Yes, in my opinion you do need a neuropsychologist. Psychologists do not do the same degree or intensity of testing and ADHD, unfortunately, is sort of a default diagnosis. It's the first one most of our kids get, even when other stuff is going on. Your child sound very rigid and I suspect more is going on than any sort of ADHD, although ADHD is probably part of a mix. ADHD rarely stands by itself.
A neuropsychologist has better testing and knows more about neurology, which is closely tied to psychology, then a plain psychologist, PhD or not. I would keep digging because the treatment isn't working. There are many disorders that present as ADHD when the kids are young, but are actually more complex. I would go there. My motto is "Better to be safe than sorry." And many of us, including myself, have lived to be sorry that we didn't do more earlier.
medications help some k ids. They don't help others. They can even make things worse. It all depends on what is wrong with the child and the child's body chemistry.
