The problem with going by the percentage of shared DNA is that different relationships within a family will share the same approximate percentages of DNA with each other.
For example, you can see in this tree below, the numbers in the red boxes being the percent of shared DNA, that you would expect to have about the same amount of common DNA with your granduncle as you would your first cousin and grand nephew. Half-siblings would share approximately 25% DNA, although that isn't a relationship listed here. See more information here.
23and me list[s] half siblings as 17% to 34% range... So [why are they] saying we are cousins at 13.57%?
The answer lies in your statement. They are saying you are first cousins, because you share the amount of DNA they would expect from 1st cousins, grandaunts/uncles, great grandparents, or grand niece/nephews. The amount they would expect from half siblings is 17-34% (or about 25%) as they have stated, and you do not fall within that range.
A way to help narrow down this unknown individual would be to compare his or her DNA to another relative such as one of your mother's parents. For example, if I wanted to add more evidence this person was your 1st cousin via your mother's side, I would compare her DNA to your mother's parents and expect each of them to be about a 25% DNA-in-common match. If that were true, then compare them to your mother, and if the match is about 50%, then that person would be your mother's daughter.
Note, that I wouldn't expect that to happen since this person does not share the proper amount of DNA with you to be a half-sibling in the first place, so you may want to be careful how you use the information you gather until you have a very thorough understanding of how it works.
I see you mentioned your mother is getting a DNA test. If this person is your half sibling, it should be a 50% match with your mother. If this person is your 1st cousin, it should be a 25% match with your mother. Remember that those are not the only possibilities for those percentages, but they are the only percentages for those possibilities.