Rachel, I hate to tell you but you have a boy. Your carpet is pretty much doomed. We bought new carpet again when same son was 13. As the installers left, he came in bleeding from a bike wreck. First stain when the carpet was less than an hour old!
I'm sure medical advice has changed much over the last 23 years, but milk made a difference for us. Probiotics had never been heard of back then, but I can see how they might help.
Two of our nephews had the same problem. They are now 17 and 6. The 17 year old tried every formula there was and then just kind of grew out of it. The 6 year old ended up on some kind of prescription formula that cost a fortune but really helped him. I didn't even know there was such a thing as prescription baby formula.
Nap when he naps if you can. House work can wait. And remember, your the Mom. Mom knows stuff. If something doesn't seem right to you, pester the doctors until you get an answer that works. Get other opinions if you need to do so.