A lot of the story is episodic, with a new spiral phenomenon appearing at the start of the chapter, and as often as not, each chapter ends with some sort of respite or return to relative normalcy for the surviving characters. Then the next chapter repeats the same movement towards a new threat, followed by eventual relief, twisting the screw a little bit more. And after all, a screw is just another form of a spiral.
Not only that, but a theme of the series is that the closer a person gets to the center of a spiral, the more intense and horrifying things get. As the stories continue to the end, the events become more and more catastrophic.
The mosquito-women fit in with the spiral theme because the mosquitoes that attacked them flew in a spiral formation and they fed with spiraling drills, but at first a reader might not be sure how the babies fit in. But babies in the womb curl into a fetal position, a spiral shape. It could also be a reference to the twisting that umbilical cords are subjected to, and the "spiral arteries" that supplies nutrients during pregnancy.
Uzumaki is already pretty terrifying, but it only gets worse when you realize the in the beginning, the story was being told after it happened. The main characters are both petrified and sitting beside an Eldritch Abomination at the end. Together.
The blueprint of the body is a spiral. (DNA) The building block of the body is a spiral. (quaternary protein structures)The lifeline of the body is a spiral. (umbilical cord) The way we perceive our world is because of a spiral. (cochlea - hearing, optic nerve and ocular receptor arrangement - sight, fingertips - touch, tastebuds - taste, nasal receptor arrangement - smell) You are made of the spiral, made from the spiral, depend on the spiral and live because of the spiral. You arethe spiral.