It's unfortunate you were disappointed in your pediatritian; it sounds like what you wanted was confirmation (which you got) that he might have adhd and a referral to a specialist. I don't think the pediatritian would have been the one to make the determination for sure. They're generalists, not specialists.

I do think some of your issues may be getting in the way as "behavioral problems" is not a bad thing. If he does not complete tasks, that's a behavioral problem for some people as opposed to an indication of adhd! That's why the doctor offered a behavioral/reward response. There's no hard and fast way to determine if your son needs meds. No doctor is going to look inside his head and say, "Aha! I see where the problem is and have the exact med to solve it". You might want to go with him to a children's behavioral therapist and together work on some non-medical ways to see if you can help him learn to focus, pay attention, and complete tasks; those are behaviors and all behaviors can be learned! Whether or not meds might help is an "additional" thing to consider after trying some regular things.

But presumably if the school sees attention problems like you have described, they too could help teach him skills and learn to stay on track (since he's there the majority of his day and that's what they are in business to do) and if those don't work, a child psychiatrist/specialist could add meds and see if they help. But no matter what a specialist concludes, the school will probably be involved in some way to help your son.