Your hen could have had a couple of things going on. The pulsing vent is not part of broodiness (at least not with my hens), so she probably did have trouble passing an egg. But if her vent is not pulsing any more, maybe she did pass an egg, broken egg or soft shelled egg. The puffing when you look in on her and returning to the nest box does sound like she is broody though. The ky shouldn't cause an infection, but on the off chance that she had an egg break inside her means you might want to keep checking her vent for any sighs of infection like discharge. There are threads that describe flushing the vent with vinegar and water after the hen passes an egg that broke in her oviduct. I hope she is fine now.
I bet you did not envision raising chickens would involve performing gynecological procedures on your hens. lol