Is it possible you're trying to get too much done when he wants your attention? I know, for me, that was always a bad combination. I would always set aside time for my kids; the chores could wait.
I know a lot of people are against playpens, but for my sanity and my children's safety, if I needed to get something accomplished or even just needed a shower, I would put them in there with a few toys or books. They would be fine and they learned they were able to do things quietly and on their own, not always rely on me for entertainment, and not always have to run around, etc. Boundaries and routines were put in place at a VERY young age!!!
My sister and I raised our kids totally different and it definitely shows - I raised mine a lot like my Mom raised us; my kids are well-behaved, quiet when they have to be and people enjoy being around them. Unlike my sisters' kids - out of control, have no concept of quiet time, and people do not like being around them for extended periods of time. And I'm talking about ages 20+!!!
As for not wanting to take him to a doctor - is it because of not wanting to put him on medication? Because I totally get that!! I wouldn't either! BUT, maybe if he is borderline ADD or ADHD, the doctor could give you suggestions on how to handle him WITHOUT medication. There are methods that do not always involve popping pills, foods to avoid, etc. It may just be something worth researching. Plus, it could help your son in the long-run!!
Good luck!!