Your son sounds smart and active and maybe he has ADHD. Search for Hallowell - he has a great free newsletter. Medication can help but might not be needed until there is a problem with learning or you can't alter his environment to keep him safe and happy. Exercise and good nutrition have results similar to medication.
I just saw an episode of Dr. Oz's show on this subject. Apparently kids have a 1 in 3 chance of ADHD if a parent has it. And you don't outgrow it, you just figure out a life that works better for you than the rules and situations we put on kids. Dr. Hallowell wrote a book on marriage and ADHD, and so did one of his colleagues, Melissa Orlov.
Kids need a lot of exercise (actually we all do) or they will drive you crazy. I took mine out in all weather. If I was exhausted or the smaller ones were sleeping or sick, I'd park by the ball field and have the wiggly one(s) run the bases. Our neighbors let their kids play outside unsupervised as preschoolers but my kids with adhd needed supervision for many more years than that and even a closer eye on them as teens because of their impulsive behavior and creative but sometimes dangerous plans. They still need snacks and breaks and routines (I still need that too and I'm grown).
Your 3 year old sounds smart. He learned how to get attention in his home. And he knows how to ask you to mirror his language and get validation. He might enjoy a recording device or even a simple kid camera to document what is going on in his life. When he gets repetitive, you could ask him to make a recording and play it later. Parenting got a lot easier for me when my sons could read and write to express themselves - something a smart kindergarten teacher predicted would happen.
I have a special needs child too and it was frustrating when the healthy kids were jealous of the attention given for having problems. The same thing would happen when one had a fever or the flu. They still get annoyed and they are older now. I try to spend one on one time with each kid. It is really hard to keep the family focused on something other than the special needs child and to keep up my energy and positive attitude. I appreciate your post because I need to do a better job of that in my own house. I needed a reminder.