I agree with acecia that it maybe reflux - when infant wake up frequently in the night reflux maybe a cause. As acecia said elevating the mattress may help - here is some additional info on reflux (from http://www.askdrsears.com/html/10/t106004.asp):
Clues that your baby suffers from GER enough to need treatment are:
Frequent spitting up or vomiting (not all babies with GER spit up)
Baby isn't outgrowing the "colic" and/or spitting up
Frequent blasts of crying that are painful cries, not just baby cries
Your gut feeling tells you that your baby "hurts somewhere"
Bursts of night waking "as if in pain"
Colicky, abdominal pain after eating, even as long as one hour afterwards
Poor sleep habits, restless
Writhing as if in pain: drawing up legs, arching back
Erratic feeding patterns. Refuses to feed or wants to breast or bottle feed all the time.
Frequent "wet burps" or "wet hiccups"
Throaty noises: swallowing noises, choking, gagging
Frequent, unexplained colds, wheezing, and chest infections
Spits up like a "volcano"
See http://www.askdrsears.com/html/10/t106004.asp for more info.
For the swaddling here is a link to by Dr Karp http://www.youtube.com/watch?v=G6KnVPUdEgQ He shows a trick to help the baby remain swaddled (and not wiggle out).