By making himself sick do you mean he's spitting up? That's fairly common among newborns, for a variety of reasons. I'll mention a few here, although it's definitely something worth talking about with your pediatrician at your next check-up to make sure there's no acid reflux or other reason he might be spitting up more than normal, and to make sure he's getting enough nutrition (as well as for some suggestions for how to help!). Try to guess at a measurement of how much he's spitting up if you can before that.
If your baby is eating too fast, one possibility is that there's too much milk there when he eats. This could either be because he's eating too infrequently, so there's a lot of milk there AND he's hungry; or because Mom's producing more milk than necessary. Mom can usually tell if that's the case, both because it probably will hurt eventually, and he will not eat all of both breasts.
It becomes harder to eat as he gets further in, so the strength and speed of the sucking will be less of an issue - but if there's a lot there, he's getting a lot. If Mom is planning to pump, this might be a good time to start - try to plan a time between feedings near to the next one where there is a decent amount of milk, and take 4-8 oz out of each breast. That'll make it a bit harder for him to get what he needs, which may help him out, since he's got a strong sucking reflex.
You can also encourage him to eat only one breast per feeding; this ensures he gets a proper proportion of hindmilk to foremilk. If he's getting foremilk in too high of a proportion, this means too little fat and too much lactose, which can irritate him and make him gassy. You also may be having an issue with the letdown - is he getting sprayed a bit when it occurs? Mom can try expressing some milk without baby when it occurs (into a bowl, a towel, whatever works) to see if that helps.
If this might be the issue for you, there are lots of resources on the net for oversupply, simlar to this article.
Another solution can be to periodically detach him early on to give him a little time to swallow. We had to do this a bit with ours, if I remember correctly. You can also change his feeding position to a more upright position; that keeps the milk from going to the back of his throat and instead lets him suck it in naturally. It also would help if he had acid reflux, though that certainly should be something you shouldn't try to address itself without talking to your pediatrician.