Three is really, REALLY young for ADHD. I see you're a college student -- did you just take a class in psychopathology? When I did that, I "diagnosed" everyone, including myself, with *something*. (smile)
I have a child with autism + some other things, including attention and hyperactivity issues. DIET plays a HUGE role, and your child may have some problems digesting his food (that's the Feingold stuff, the dyes, preservatives etc you mention). He may also have some food ALLERGIES as well.
Omega 3's may help. Whole Foods sells gel caps that are ball-shaped (they're round) that can be chewed so that they squirt open in the mouth, or swallowed, and they're strawberry flavored. Check w/ your doc on dosages and make sure there's not a fish allergy first.
Grab a book from the library called, "Is This Your Child?" by Doris Rapp MD for starters.
And grab a book called "Ezzymes for Autism and other Neurological Conditions" by Karen DeFelice.
Do a google search on epsom salts baths, too. Susan Owens and Rosemary Waring are two names to google in the area of sulfation. The epsom salts baths can help with the Feingold type issues (they're related to one another).
He may also have some sensory issues (google sensory integration dysfunction). Carol Stock Kranowitz's "The Out of Sync Child" is a good first book. You *might* see your child in the pages and get some good ideas to try at home.
And have your school district screen your child for delays. It's free. If he's already three, you'll have to go through the special services (special education) dept and not Early On, but have them screen him to put your mind at ease.