I'm looking for an authentic water jug from Mexico, What's it called?

you are looking for a "Cantarito" which is usually the earthen jug for holding water at the table, they have a smaller opening . A "Cantaro" is a larger version for storing more water. An "Olla" has a much larger opening than a cantaro and is used primarily for cooking, not for holding water, Ollas are usually glazed to withstand heat.