I think you won't really know what's going on without doing more testing. There could certainly be other reasons for the tantrums and lack of self control that aren't ADHD. Full neuropsychological testing would give you the most information, but an IQ test could be a start as well.
In the meantime, are you working on ways of dealing with the behavior? I learned a lot from "The Explosive Child" by Ross Greene. He also has a website
www.livesinthebalance.org/. The "collaborative problem solving approach" has worked well for us. I think the talking it out, problem-solving approach works well for gifted kids.
Another book often recommended on this site to help with difficult behavior is "The Nurtured Heart Approach".
