I gather that you are not in the USA, so you may have different special education regulations and services where you are. Your school may have a school psychologist or educational psychologist who can conduct further testing, such as academic achievement, memory, and even emotional/psychological. That would be one avenue. Another would be to ask your pediatrician for a referral to a neuropsychologist, who could do similar testing, and possibly additional measures as well.
His negative self-concept and perception of himself as stupid actually have some diagnostic value of their own, with regard to learning disabilities. They suggest that he is aware that there are skills which "ought to be" simple for him, which mysteriously are quite challenging--a response to the gap between his intuitive understanding of his high level of cognition, and inexplicable (to him) obstacles (aka the learning profile that could be described as learning disabilities) to demonstrating that cognition in ordinary activities.
