Charlton clocked 7.67 seconds in the hurdles to shave 0.01 off the previous world record set by Susanna Kallur 16 years ago.
"I heard the announcer say something that sounded like 'world record', but it didn't hit me until I saw my name and time on the clock," Charlton told World Athletics.
"I can't describe that moment. When I saw that clock, I felt relief. When you set a goal and work towards it all year, and then you achieve it, it makes you feel you're on top of the world," she added.
Two-time world champion Danielle Williams was second in 7.79, while Tia Jones, who had the same time as Williams, was given third place.
Kerr, the gold medallist in the 1,500 metres at last year's world championships in Budapest, ran eight minutes 0.67 seconds to break the previous mark of 8:03.40 set by British running great Mo Farah in 2015.
Grant Fisher broke the American record in finishing second in 8:03.62.
