Here’s another year old article that came out in response to this.
TLDR: You should not worry, and the only people who might think about worrying are those drinking 12 cans of diet soda a day — so basically no one.
"Our results do not indicate that occasional consumption should pose a risk to most consumers," said Dr. Francesco Branca, director of the Department of Nutrition and Food Safety at the WHO, during a press conference in Geneva. He said the problem is for "high consumers" of diet soda or other foods that contain aspartame. "We have, in a sense, raised a flag here," Branca said, and he called for more research.
But the U.S. Food and Drug Administration says it disagrees with this new classification, pointing to evidence of safety. In a written statement, an FDA official told NPR that aspartame being labeled by the WHO "as 'possibly carcinogenic to humans' does not mean that aspartame is actually linked to cancer."
The WHO has long set the acceptable daily intake, or ADI, of aspartame at a maximum of 40 milligrams per kilogram of body weight per day. So, a person who weighs 60 kilograms (about 130 pounds), could consume up to 2,400 milligrams per day, which is roughly equivalent to 12 cans of Diet Coke — much higher than most people consume.