Personally and professionally I think 3 is too young to be diagnosed with ADHD. Many preschool aged boys are typically overactive and may possess a particular learning style that may be perceived as ADHD - my 4 year old included. Fortunately I have plenty of experience with ADHD students to know that my son is not one of them.
My question to you is what were the teachers' education background at his former preschool? Often many preschools have teachers with little or no educational training or degrees - which is a shame. Preschool teachers without the experience and knowledge about child development may have a difficult time #1 devising methods to work with an energetic learner and #2 understanding typical behavior vs. atypical.
I do believe in early educational intervention and testing. It is beneficial to have children tested early to ensure greater success in school. I myself have referred 4 year old children for ADHD testing - but those behavior indicators were extreme.
With that my advice to you would be to talk to his pediatrician. Explain your own condition and experience and s/he may tell you if there is a genetic link and would be able to refer you best.
If the Dr. agress with ADHD testing at 3.5 then I would heed that advice so your son could get what he needs to succeed. It would be a huge diservice to your son not to get him help if he genuinely needs it because of your own experience.
Keep in mind that testing does not mean he will be diagnosed with it.
Should he be diagnosed with it you need to know that much has changed in the educational system since we were in school. Educators are trained to include children with IEP's similarly to children without without negative attention brought to that student. Labels are not the same anymore either. Having a correct diagnoses of ADHD will only help.
Please let me know if you need any further advice. I do wish you the best.
A.