She won't have any problems breathing in a tummy to tummy with her face against your chest as long as her airway is not restricted. The thing to avoid is having her chin tucked up against her chest (with shoulders slumped or rolled forwards).

What sort of sling did you make? A ring sling? A pouch? If you made a pouch, did you size it for your body correctly? An incorrectly fitted pouch will not only be less comfortable for bubs (she will swim in it!), but will also cause drag on your shoulders. If it is a ring sling, try tightening the top rail more, and tightening the central fabric so that her torso is better supported and snug against your body without slumping.

There are some good video tutorials on youtube for adjusting and wearing slings.