Ojo:
I have a 16 yo boy with pretty severe ADD. He has been on medication for about 6 months and it works great and he is happy with his school. He is way behind his peers in the classroom due to his condition and some serious slacking on his part, but is an otherwise intelligent and fully functioning person who is on the right track.
However, getting to this point has been years in the making starting when he was 5. Many interviews, psych evals, electrodes, testing, different schools, and lots of heartbreak along the way. Nonetheless, still a very rewarding parental experience with knowledge and acceptance of my son's true identity and personality.
Now, I doubt your son's ultimate diagnosis is anything close to what my son's is, but some things are still going to apply from my experience.
Public school: No matter what the law says and what school says, there is only so much that those guys can do with the resources they have. It is certainly worth checking out and trying, but they deal with certain things better than others and we did not have any success there.
Home schooling: We tried this too, but it is hard to sustain and educational effort consistently and it lacks the interaction with peers and that seems like it would be a big deal for your son.
Growing up: This helps as the child becomes better at expressing their frustrations and guides you as a helper as they develop communication skills and maturity. It is hard to imagine that with effort and a nurturing upbringing that issue will persist into adolescence or even adulthood to the point where it inhibits your goals for his happy life
Diagnosis: We had a few wrong ones along the way by competent professionals. The most egregiously wrong one was a diagnosis of severely impaired gross motor skills. We tried some physical therapy after the diagnosis, but the exercises were so hard my wife and I could not even do them, so we ended that after only about 6 weeks. Long story short, shortly after that we noticed that he really liked to climb trees at school. We guessed it had something to do with avoiding contact with others and it otherwise engaged him. We were concerned since he had "severely impaired gross motor skills" and we didn't want him to hurt himself, so we got him into rock climbing in a gym with ropes, so at least he wouldn't fall. Well it turns out out he has exceptional gross motor skills and despite being a bit of a space cadet when it comes to putting in the time to read and solve routes due to his "condition" he made up for it with exceptional coordination and outside the box route solving and from the time he was 8 to now has been a competitive rock climber in all disciplines and ranked in the top 50 for his age group in the US and has also become a really good skateboarder.
Another one was a completely wrong diagnosis of dyslexia. Turns out that he was so far behind in school, he didn't understand the questions at the time and could not express the issue to us. Learning issues yes, but no dyslexia.
So moral of the story is don't put too much into any diagnosis right now. There will be more and you will find what will work best. BTW, The psych eval was very good and did get us the info we needed to really deal with the issues he was facing. He was older, I want to say about 10, so he was able to have a really good one on one with the Dr. that I don't think he could have handled when he was younger.
Just don't expect answers all at once. Your on the right track.