My son's dysgraphia / dyslexia was diagnosed by a neuropsychologist. Had we waited on the school to do further testing than the IQ tests, he still wouldn't be diagnosed or receiving appropriate accommodations and services. If you can at all afford it, I'd highly recommend private testing.
At the beginning of 2nd grade, he was a year behind in reading, could not write legibly, had a speech disorder, and had difficulty holding a pencil appropriately. Because he was not "far enough behind" in academics (needed to be a full 2 years behind), the school refused to test, despite requests from us and his teachers. After we had a private diagnosis in hand, the school accepted the diagnosis and we started the process to get him admitted into special ed with an IEP and appropriate services. We started speech therapy privately until the school finally had it as part of his services.
There will be others who will be able to speak directly to your scores, but I did want to chime in with what our experience was.
