Hi E.,
I have had pain in my wrist at different times and I was going to suggest a chiropractor as well. It turned out for me that the problem was really in my neck and shoulder (the nerves that go to the hand/elbow run through that part of the neck and was giving me "false pains"). I knew that I felt tired and sore in my neck and shoulders as well, but I didn't connect the two.
If you are primarily carrying your son one side and not trading between the two, you might be causing a stress injury on the dominant side. Carrying a heavy load on one side also tends to put the body out of alignment - especially as women as we tend to put a hip out to help carry the load which puts our whole spine into an 'S' shape.
If you can, try carrying your son on the other side some. It will take some getting used, if you aren't doing already. I find that being able to trade my daughter (18mo) from one side to the other can bring some relief.
You also might try a carrier of some kind - I have a Baby Bjorn, which I love, but it sounds like your son might already be too large to that one, but there are others like it that can accomodate larger/heavier babies and also side-carriers, where the baby is positioned on the side, just like you might carry him, but the weight is distributed better. There are also back-pack style carriers that might work. We have one of those now for my daughter and she loves it. I was afraid that she was so used to being in my front that she might not like being on the back, but she loves it.
Anything that gets him out of your arms (but still nestled with you!) will give your arm some time to heal.
I hope it gets better soon!
P.