What motion sensor to use for human breathing
Such motion sensors are commercially available. They have a transducer that takes the form of a large, flat pad. This is put under the bedding, and the infant lies on top of it.

It is coupled to some transmitter that will activate an alarm on a receiver if the transducer stops detecting movement.

So, that is what the successful, commercially available product looks like. 

A good starting point would be to survey these, get one, and take it apart.

In a university challenge project, you don't have to beat a product in the marketplace, but of course whatever you come up with inevitably does get compared with what is out there.

All products have limitations because removing all imitations means skyrocketing cost. If you could find one or two limitations of the existing product and improve on them, then you have a "story".

Sometimes it's enough to improve on some limitations while introducing or increasing others. From the point of view of a consumer who cares about the limitations you improved, and does not care about the worsened ones, this is an improvement and in the market as a whole, it represents a broadening of the available choices.

Do not think you have to monotonically improve something; just making different design trade-offs is interesting.