"swift glance" is correct and usable in written English.
You can use it to describe a glance that is very quick — it usually is used to suggest that the glance did not allow for much detail to be seen. For example, "He gave the room a swift glance before making his entrance."
A swift glance at the woman and Helen realized that she was not angry but desperate, and that Helen was now involved in an intimate, silent dialogue with her.
A swift glance through the current and imminent lineup of openings indicates a neat baker's dozen of American titles alighting in the British capital for the late-spring/summer season.
Even a swift glance under said oak tree, which sits directly in front of the Augusta clubhouse, at any given moment – and as the Masters rages on ahead – is revealing.
A swift glance through the list of singers who have appeared on that tiny stage produces names like Janet Baker, Ann Murray, Sergei Leiferkus, Geraint Evans and Alessandra Marc.
For most modern readers, Early Modern English poses enough semantic and syntactic difficulties to require editorial annotation that swift glance to the bottom of the page that informs us that many familiar words, such as virtue and honesty and credit, had different meanings then.
Sadly, a swift glance at Battleborn shows that Blizzard were right to stick to the simplicity suggested by Team Fortress 2. Gearbox's entry into the genre turned out to be a confusing mess, with too many systems layered on top of each other leading to overlong, grindy matches.
I shot her a swift, horrified glance of apology, dashed inside one of the stalls and hid there for 10 minutes to give her plenty of time to flee.
Cersei's despair as she cradled her son, the swift, subtle glances between Margaery and Olenna, two consummate players of a consummate game, the raw, empty look on Arya's face at the season's end.
At first glance, swifts appear to voluntarily restrict their own reproduction.
At first glance, my swift and admittedly crude dismissal of an icon of 1960s counter-culture might seem the product of my youth, immaturity and overall lack of ability at the time to appreciate the positive impact that Joan Baez and those like her had on the generation that followed them.
I remember his sad glances, his swift and final exit.
