As a mom of a child with ADHD, dysgraphia and dyslexia, I agree with all those that recommend further psycho-educational or neuropsychological evaluation. It could be ADHD along with other LD's or it could be stand alone LD. If so, specialized instruction and accommodation would be in order - with or without meeds, depending upon whether or not the ADHD diagnosis stands.
I also agree that for complex kids, a pediatrician may not have the expertise needed to help you treat/manage ADHD if it exists. I would recommend a developmental pediatrician, psychiatrist or neurologist that has expertise in LD's to help guide you. They'll be better able to tease out what is playing havoc with your son.
Also keep in mind that if you are in a public school, they do not have to accept outside testing. The law says they only must "consider" it. Most likely, they will do their own evaluation to determine if he is eligible for accommodations and services under special ed. Given he is so bright, they may be reluctant to qualify him. You may want to consider a strategy of letting the school do the initial evaluation and if you want more info and disagree with their results, you could then have private testing done. To get the school testing started, write a letter that explains your concerns and very clearly and directly request a full academic and psychological evaluation to test for the presence of learning disabilities particularly in the area of written expression. Under the law, they must conduct the testing within 60 days or so (varies by state), present you with the report, and determine if he is eligible for special education.
Best of luck.