I wore Burt's lip balm for YEARS, my favorite, loved the peppermint oil in it. Then I suddenly out of the blue became allergic to it! Every time I put it on my lips ballooned up huge and burned like mad for a whole day with red rash around the edges- AWFUL!!. I read about this happening with other women and Burt's. Turns out the essential oils were the offending ingredients.
Now I use Chapstick moisturizing chap stick, as it has sunscreen and no problem ingredients like peppermint oil or menthol. It amazes me to read the ingredients now and see how many lip balms have menthol and/or essential oils of some kind. Most do.
There's also a peach flavored balm from the health food store I can use safely.

I read somewhere that the more often you apply lipsticks and lip balms, the less the natural lubricant glands on your lip skin work anymore. They normally put out some sort of natural waxy protective stuff. (apparently breast areola areas do this as well, as a way to protect your sensitive skin while nursing). I remember when I was addicted to lipstick for years- when I didn't put it on my lips got terribly chapped within hours. When I weaned myself from the goo, it took weeks but my lips began to be naturally soft and chap-resistant again. They also got their natural pink color back again gradually.

Funny story- when I met my DH 7 years ago, that was when I had to break my lipstick addiction- literally because it was getting kissed off every few minutes and it became just too much of a hassle to keep putting lipstick back on!
Now I use the chapstick a few times a day, but i try to not have it on all the time, or for bed.
Try going Commando!!!