Upon fact checking this claim, I found numerous articles questioning the usage of lip balm on chapped lips, which was similar to the title of the article they linked in their claim. Google even gave me an "instant answer" when I searched their claim and agreed with their statement. From just a simple Google search, I was able to get the idea that this claim may be true; however, strictly googling this claim shows bias, so I looked more into it.
After reading the article linked in the claim, I can summarize that this CNN article did not explicitly state that lip balm is making your lips more chapped. The article, however, did mention the science behind chapped lips (thus, the causes of chapped lips), common ingredients in lip balms that are irritants and may contribute to chapped lips, as well as what to use instead to prevent chapped lips. This information is not enough to state the broad claim that all lip balms make lips more chapped. While it is true that there is correlation, I feel as though lip balm has an indirect effect on chapped lips (i.e. some people may be allergic to certain common chemicals found in lip balm, like Beeswax, which can cause drier/itchier lips). However, the article retrieved their information from doctors and reputable institutions, so I decided to look into the other articles I Googled earlier.
I found this article that was updated in July 2024 and reviewed by Michele Farber, a New York-based board-certified dermatologist that states “It's possible, but it depends on a number of factors”.
https://www.byrdie.com/does-chapstick-make-your-lips-more-chapped-6825041#:~:text=%22These%20'medicated'%20lip%20balms,out%20the%20lips%20even%20more.%22
Similar to the CNN article, this article gives multiple factors and situations in which a lip balm may cause dried lips. For example, menthol may initially give a relieving sensation by exfoliating the lips (and removing dried cells), but eventually damage the thin protective layer on the skin that is responsible for moisture. This article was medically reviewed, along with the fact that the author has a Master's Degree in Public Health Nutrition, making this a reliable second source to the original claim. Overall, this claim is true in that some lip balms do indeed contain drying ingredients, but not all.