Hello booho,
You are correct. Everything that comes before "그 아이" is just a description of what this baby was like.
More specifically, the sentence is describing how this baby was big enough to make "그 여자"'s (the mother who was pregnant with the baby) already narrow shoulder stand out even more during the 9 months of her pregnancy. The mother carried the baby for 9 months during which her narrow shoulder or ""그 여자의 좁은 어깨" looked even more noticeable or "더 도드라지게 만들 (정도로)". Literally translated, "(it is) the baby with whom the woman was pregnant for 9 months, all the while swollen up to the point where her already narrow shoulder looked even more noticeable. "부풀다" simply means "to be bloated, swollen up, inflated, etc.", and "둥글게" here is a mimetic adverb giving the readers a rather visual idea of how "round" the mother's belly became when she was pregnant with the baby.
Hope this helps.