Hmm, newborns do breathe kinda funny, but he's out of the newborn stage now...it can take them a while to "settle in," but you should take him to his pediatrician just to be sure. You could even tape record/videotape what is worrying you, so his doctor knows exactly what you're talking about.
It will help to take your baby to bed with you. Sleeping with their babies, mothers act as a sort of breathing pacemaker. Another good thing to do is to carry him at least 4 hours per day in a baby sling or other infant carrier that keeps him close to your heart. This helps him to "organize" all of his systems, as he is hearing and feeling the regular, rhythmic patterns of your breathing, heartbeat, etc.
Sleep sharing with babies is at least as safe as having them sleep in their cribs, as long as you follow the rules. Go to askdrsears.com or do a google search to find out how to do it safely.
But these things do not come in lieu of taking him to see his doctor. Do them in addition to.
I got this advice (sleep sharing, baby wearing) from Dr. Sears. You might benefit from getting a copy of his Sears Baby Book. Just a couple of dollars on amazon.com for a used one!
L.