It is an English word, including an American English one.
A way to check and see if something is used in American English is to check an American English dictionary, or one configured to give American English uses.
Whereas dictionaries are not geared toward specific collocations, the first two dictionaries listed below give example sentences with analogous collocations. One could check Ngrams for current usage of a specific collocation.
ODO US English definition
M-W dictionary definition
American Heritage dictionary definition
However, most good dictionaries will specify whether something is an AmE usage or an BrE usage, including the
Cambridge dictionary public school, which is totally different in the UK and the US.
On second thought the Cambridge AmE dictionary does not give both meanings.
Although both the M-W For Learners and American Heritage does. As does the ODO of British and International English, the three I cited at first. In fact the ODO AmE also gives both definitions.
So it seems Cambridge chooses (at least sometimes) to particularize, while others tend to generalize. I prefer the Cambridge for many of its definitions, but around here the ODO seems more popular.
Fag is another word that has BrE-specific (if not AmE-specific meanings), and all the dictionaries listed here touch on both.