I stumbled across this in new posts...you mentioned a squeek...look up laryngomalacia and tracheomalacia and tell me if you think it sounds similar. My son has laryngotracheobronchomalacia (quite a mouthful!) and his breathing as a newborn and infant were terrible, strangers would approach me at the store and ask if my baby was okay. Airway malacias are not always a problem, sometimes it's just a slightly underdeveloped airway that corrects itself over time. In my son's case it was associated with his genetic syndrome, but we didn't know for that a while.
If it sounds like it could be malacia, keep him off his back! He should be on an incline, upright, or on his tummy to help keep his airway open. Does he have reflux at all? Reflux and malacia tend to go together because the baby has to work a little harder to breathe, they use accessory muscles which then aggravates their little tummies and they reflux. Another reaons why back sleeping is worse for them.
It might not be malacia, but I thought it was worth mentioning!