"alarming headlines" is correct and usable in written English.
You can use it to describe headlines that have a shocking or urgent tone. For example, "The newspaper was filled with alarming headlines about the climate crisis."
The past week has seen a flurry of alarming headlines.
In the wake of alarming headlines, an obstacle course of cumbersome but laudable security precautions unrolls at airports, leading many of the earth's seven-billion-odd inhabitants to resolve to remain earthbound as much as possible.
WHAT with angry parents, alarming headlines and crusading politicians proclaiming the dangers of MDMA a recreational drug more commonly known as Ecstasy it takes a brave, or foolhardy, individual to go against the grain.
That claim fed alarming headlines.
Others followed suit with comparably alarming headlines.
Gossip sites posted alarming headlines: "Taylor Swift's Boyfriend Shuffle," "Maybe You're the Problem," "Ex-Boyfriends Beware".
Wonga.com, an online lender offering short-term loans, stressed that the publication of the "alarming" headline figure of 2,689% APR on its website was a legal requirement but bore no resemblance to the reality, due to the short-term nature of loans.
But editors of magazines with less spectacular budgets, like Men's Health, are increasingly paying more attention than ever to the cover, which with its magical mix of images, buy-me colors, stimulating promises and alarm-sounding headlines can induce readers to pluck a magazine off a supermarket or newsstand rack.
Even more alarming were the headlines on sites like Fox News, reporting that more people were killed in Chicago then coalition forces in Afghanistan!
"There would be headlines, alarms and calls for action".
Those customers may be alarmed by the headlines about the health of Irish finances and by speculation about the break-up of the euro.
