The phrase "tensions heightened" is correct and can be used in written English.
It is typically used when discussing a situation where emotions are running high and conflicts or disagreements are becoming more intense. Example: As the negotiations continued, tensions between the two countries heightened, making it difficult to reach a resolution.
Meanwhile, tensions heightened around the PK5 Muslim enclave in the capital, Bangui.
Tensions heightened in the daily interactions between NYTD and the Times.
As the night wore on, and tensions heightened, some protesters tried to shut down a freeway, while others broke windows and refused to disperse when ordered by police.
As international tensions heightened during the summer of 1914, Germany made plans to besiege France by crossing Luxembourg and Belgium, despite their neutrality.
Tensions heightened further in September when rumors began to race through Urumqi that Uighurs were stabbing Han residents with infected syringes.
Jonathan Blitzer was at the U.S.-Mexico border as tensions heightened after the U.S. fired tear gas at migrants seeking refuge in America.
The only effects were to fan political tensions, heighten exchange rate uncertainty, and upend the global trading system.
In Syria, the tensions heighten the risk of conflict between Turkey and Syrian Kurdish militias that — theoretically, at least — are on the same side in battling the Islamic State.
As tensions heighten, two women venture out of their houses to tend a nearby community vegetable garden, only to find it in ruins, plundered and destroyed by scavengers.
Irish police are investigating a bomb threat to a government minister's office as tensions heighten over the introduction of water charges.
Pakistan-based Islamist militant group Jaish-e-Mohammad have claimed responsibility prompting India Prime Minister Narendra Modi's vow for retaliation as tensions heighten between the nuclear-armed rivals.
