BabyBlue(s):
ADHD is uncommon to diagnosis that young, although it's not unheard of. Unfortunately, my experience is that docs diagnose ADHD one of two ways: either (a) they do a thorough famly history analysis, along with a battery of diagnostic tests on the patient, and/or (b) prescribe ADHD medications, and see if they work.
With a 4YO, you could get a family history that indicates ADHD, but it would be hard to perform the diagnostics on your son to confirm. And ADHD medications are powerful pyschoactive stimulants, and could be rough on someone so young. So, while IANAD ("I am not a doctor"), it stands to reason that your docs are probably right on the medications.
That said, there are other things you can do. The biggest "lie" told about ADHD is that "medications will cure it". No, medications will NOT cure ADHD. It cannot be cured. medications will help the brain function correctly, but proper treatment for ADHD is medications combined with effective therapy to teach coping mechanisms. The therapy is just as important as the medications, maybe more so. In my own case, I wasn't diagnosis'd until I was over 30, but had learned coping mechanisms on my own that helped me be somewhat functional before I was diagnosed and started medications.
So, even if you can't get medications for your son, there's no reason that you can't start working with him right now on learning the behavioral side of ADHD treatment. The biggest challenge at that age will be frustration, which can lead to anger issues. So anger management and basic organization skills should help. There are quite a few good books on this that you could read; I don't know of any that are specific to very young ADHD sufferers, but someone else here might know.
Also, I would be careful on the diagnosis, since symptoms of ADHD can mimic (or overlap) symptoms of other illnesses and disorders. At 4YO, I think it would take a pediatric psychiatrist or neurologist to accurately diagnosis something like ADHD (over something like Bipolar or other issues). I would caution you to seek medical advice from someone you trust, who is reputable, and most of all qualified to make such a diagnosis. Barring that, the safest thing is to stay away from the medications and start learning coping mechanisms (both for your son, and for YOU).
Just my humble two cents - hope it helps.
Mikey