Not a teacher.
"Shots" are the American term for a small portion of liquor served in a small glass. 1.5 US Fl. Oz. (~45 ml) is the typical size.
Shots are usually not sipped, but thrown into the mouth and swallowed quickly.
In this excerpt, the author is saying he is surprised to see this woman drink like that. That it was out of character for her to drink so much so quickly. (Multiple shots)