Hi N.,
Wanted to respond as I've had a similar experience with my 2nd daughter who is now 7 months old. When she was about 5 weeks old she had horrible eczema on her face and huge amounts of gas. I also went off dairy and it helped a ton. Eczema cleared up and the pain associated with all the gas went away. She continued to have lots of gas but it was much better. If you're off dairy completely you have to watch out for anything with whey or casien in it too, just in case you didn't know that. My daughter is also exclusively breastfed. She had horrible smelling poops and smelly gas too, which is shouldn't have. breastfed baby poo doesn't really smell, or it's not supposed to!
For relief the best thing I found for her was a product called Colic Calm. You can find it online and maybe at whole foods. it's a gripe water, all natural, but also includes activated charcoal which binds to the excess gas and neutralizes it. Since the gas never completely went away I tried going off wheat and soy, which didn't help and then I had her tested with an allergist and she was negative for all major food allergies, including milk. so...I took her to a pediatric gastroenterologist who tested her stool for blood, also negative. Basically she told me excess gas is difficult to diagnose.
Periodically i would add dairy in to see if the symptoms would go away but they always came back. Then a few weeks ago we went to Jamaica for a week at an all-inclusive with the girls and almost immediately I accidently had dairy. She was fine the whole week. I had dairy every day there. I was so happy the special diet was over and then we got back to the states and I had milk and the symptoms started up again. The only thing I could figure was it was the growth hormones they gives cows in this country so they produce more milk and are bigger. So last week I went and got hormone free organic milk and she's had no symptoms at all. I'm relieved that I finally figured out what it was but it is a bit frustrating that it took going to another country to figure it out! So now i'm just being careful with the type of dairy I ingest and so far so good.
Sorry...long story and who knows if your situation is similar. I just wanted to share my experience and give some ideas and support. I found that I had to continue to push my pediatrician with this. I knew something was not right but because she was thriving and didn't have blood in her stool (a sure sign of an allergy) they didn't find it to be a major concern. I guess I would just trust your instincts.
I have also had some friends whose baby had GERD and they did eventually outgrow it. They found that if they kept the baby's head elevated, even when sleeping that it helped. Prilosec was a wonder drug for them.
Best of luck to you in figuring this out and congratulations on your new son.
J.