“Row”–defined by the OED as “a noisy or violent argument”–is a useful word, being roughly in the middle between “fight,” on the one hand, and “quarrel” or “argument,” on the other.
It is definitely a Britishism–or at least, has been one since about 1930, according to this Ngram viewer chart. (The OED‘s first citation is from 1746.) I searched for the phrase “had a row” to reduce other uses of the word.
My sense is that in recent decades, “row” has generally been limited in the U.S., first, to pretentious people and, second, to headline writers, based on another useful quality: its brevity. However, this sentence appeared recently in the text of a Wall Street Journal article, in reference to a Philadelphia woman: “Mrs. Stokes, 63, was arrested twice in 2008 and 2010 during rows with her now-estranged husband.”
I searched “had a row” on Google News and had to go back about 90 hits before I found one from an American source–a Chicago classical music website. But it turned out to be a quote from a British director. So for now, useful or not, “row” is still “on the radar.”