Hi cote - this sounds exactly like the issues I had with DD1, and have been having a similar but less severe time with DD2 (now 5 weeks). With me, it is (I think) a combination of 2 things...
Firstly oversupply, which to the poor baby is like having a hosepipe shoved down his throat, which also makes them swallow lots of air, and then be sick everywhere (you should see our carpets!). When your DS pulls off, do you spurt a lot? I find BF a very messy business... . This made my DDs scream and pull back, and with DD1 she was so averse to feeding after a while that she took the minimal amount then would have no more. There are lots of tips on the kellymom site above, which is really helpful. I found with DD1 that nipple shields helped for a bit, as they slowed the flow down a little, but do read the kellymom site for other tips, as nipple shields aren't generally the preferred first thing to try (and I found with DD2 that she didn't get on with them at all).
Secondly, I think part of the pain/windy/sicky problem was internal discomfort caused by allergy to the small bits of dairy coming through my breastmilk. Think this is fairly unusual (and the health professionals seem to think its impossible), but DD1 is severely allergic to dairy, and her eczema only cleared up when we switched to a special formula at 1 year old. With DD2, we were having 3 hour screaming stretches every night, until I cut out dairy myself last week and she's like a different baby (still a pain in the neck, but you know what I mean!). So, for me, I think dairy allergy is definitely a factor (or a massive massive coincidence....).
DD2 is still a very windy baby, I think partly because I still have a lot of milk (although we are managing the oversupply better this time round), and we still have occasional vomits and amazing poos and farts (puts my DH to shame ), but much less screaming....
I would try the oversupply solutions first before cutting anything out of your diet though (and if you do cut stuff out of your diet, just one thing at a time, and give it a few days to see any change).
Just one other thought as well... how often is he feeding? Just that DD2 goes mental if I try to feed her when actually she's tired (even though, helpfully, she acts in the same way whether she's tired or hungry). So if he's feeding too often, and when he's not really hungry, that's possibly not helping things...
Hope that helps a bit... I really feel for you, its a nightmare trying to feed a screaming baby . If its any consolation, he's 7 weeks already, and I found that the BF supply issues settled down after about 12 weeks, and I actually enjoyed it then (and was very glad I hadn't switched to formula given the allergy issues!).