I'm quite careful with my lips, as they're sensitive and chap/crack easily, but occasionally (sudden cold or dry spells, etc.), I get a split in the middle of my giant stupid fat lower lip that takes a couple of days to heal. Any time anything in the lip area reaches the level of actual physical discomfort, out comes the Carmex to numb the area, make it feel lubricious, and keep me from worrying it with my teeth and tongue. Carmex doesn't so much *heal* your lips as it creates a nice, moist environment in which they can heal themselves.
Of course, menthol is somewhat drying, but I find that it balances that out by distracting me from the feeling of the big split in my poor lower lip, used to being smothered in Aquaphor and NYX Butter Glosses. And Carmex is US$2, max, at least in my area.
As to the flavor, I'm old enough to have used Carmex when it came only in tiny metal tins, and I can tell you that we've come a long way. Even the actual Carmex base is far milder smelling/tasting than it used to be. The last one I grabbed happened to be cherry, but I'd use any Carmex flavor without hesitation. Trust me, it tastes better than 90s Carmex!
Some really thick oily/buttery balm with peppermint oil or something might be better. But my lips seem to like petrolatum, so only might be. And this is $2, dammit. Not my regular lip balm, but an occasional lip necessity for me nonetheless.