Hi Natalie,
I would think pulling up the water hemlock would get rid of it, but I guess I'm wrong.
I don't think you're other weed is shallots. Maybe you meant Chives? If you meant chives or something chive like, as long as you get the bulbous part out of the ground, it won't come back. The roots below the bulb will just dissappear into the soil after awhile. If seeds are in the ground, you may get new sprouts, next year, but just dig them out. After a few times of doing that, they will be gone.
Remy

Many weeds can be beneficial, shallots, chives, onion grass may just be in that catagory...
But they must be controlled - pull right after a good rain..