Wow, this is a worrying one.

The breathing difficulty sounds a bit like my fourth child, who had asthma
that started at about six weeks. He breathed just the way you describe -
sucking in under his ribs with each breath. For the first six months, I
think I just nursed him more or less constantly, because he couldn't nurse
for long periods of time without getting tired. By then the doctor had
prescribed some medication which helped a lot, and we were able to use a
mask with him as needed. (He has since completely outgrown this, hurray!!!)

But the blueness when he cries makes me think of my friend's baby with a
heart defect. This wasn't picked up by a doctor until he was five months
old, and he needed open-heart surgery at seven months. This baby rarely
cried (constant breastfeeding and always in mom's arms) but when he did, he
would go blue around his lips. He was also unusually sleepy and tired
easily. (Turned into a very different, very lively baby after the surgery!!)

Could it be a combination of these two things? I'd really want to get it
checked out. And if it's asthma, I'd be very cautious about adding lots of
formula - I'd rather have mom pump, build up her milk supply, and supplement
baby with that if necessary.

Just some thoughts.

Teresa