The guards of the city don't attempt to bar the way for multiple reasons. They don't know the effective range and quantity of flowers needed to be infected, so they can't even tell where it exactly is, let alone set a border. Anyone intending to put a stop to it would probably be sacrificing themselves(which is possibly what the brother did, but whichever the case some remained to grow). Another reason is that the city is not quite so modern as to be able to quickly organize a large group of guards to do the work needed. That's a hefty load of logistics to handle without leaving your city defenseless to other threats. The last is, well, magic. Muggles don't mess with magic, full stop. We are in full Fae mode here, make no mistake.
On Elaina's case, she could have done more. But she doesn't have the standard protagonist's all-consuming need to help people. Also, even as a witch, you don't mess with magic. All manner of things could happen if you try to kill a magical organism that is in home turf and plugged to a giant mana battery(eg. THE WHOLE DAMN FOREST). She's a genius, but she's also exceedingly young and lacking in the stereotypical arrogance that comes with being a prodigy.
No shame in being afraid.