Do you have insurance? Most insurance plans cover what they call "behavioral health." You should be able to get an assessment (including ADHD screening, IQ and achievement testing) covered by insurance due to behavior issues/concerns. We were able to get a full battery of tests administered by a neuropsych 100% covered by our insurance.
Our insurance plan is terrible and they won't even cover neuropsych exams for autism or cognitive impairment (i.e. low IQ). It specifically mentions no testing for ADHD, learning disabilities, or developmental delay. DS's neuropsych testing was covered because he had a traumatic brain injury and had some obvious brain damage (for instance an eye that was stuck and crossed). That is one exception they make.