This article from AOPA outlines the issues with ADHD pretty well.
This article is from Canada but the medical policies are quite similar and you might find the basic information useful.
Bottom line seems to be that once you are formally diagnosed with the condition, that becomes a problem. You can't be on ADHD medications at all (within the last 6 months) and if you are diagnosed (officially) and are not on medications, you have to go through a testing protocol to satisfy the FAA that are fit to fly without medication.
There seems to be a lot of misdiagnosis of ADHD and the symptoms you describe may not be severe enough to be considered a real case (you may be getting too hard on yourself; I get sidetracked on tasks by things like shiny bottle caps on the floor, get bored easily, and if you give me a Rubik's Cube, I'll tire of it and put it down after about 2 minutes, and I've been flying since the mid 70s).
When I read about the symptoms of hard core ADHD (especially over-diagnosis of kids - it's criminal in my mind) it sounds like you would be barely able to function in the world, and your description doesn't sound like it rises to that level. I'd be wary of proceeding along the path to an official diagnosis unless you've decided it's so bad you can't function without medication, and at that point flying is out.
If you do nothing and carry on, and you have a significant case, it'll become obvious during training and you'll probably never get to the solo stage. FAA protocols are based on a diagnosis, which should be by a psychiatrist, so I wouldn't bring it up to an AME until you get to that point. I would explore other non-psychiatric therapies or techniques that could help with focus and discipline first, and would avoid the medical route unless it was a last resort. Your doctor may not have been doing you any favors by suggesting you might have a serious psychiatric condition based on some comments.