Burts Bees lip balm is a good brand, and mostly natural. Much better than chapstick that contains lots of chemicals.
There are many different lip balms made by Burts, I believe you are referring to the "Beeswax Lip Balm" in the yellow tube with the yellow cap? Even though it is almost all natural, there are two ingredients in it that might cause issues for some people:
1) Peppermint Oil
Both of these cause issues with a small percentage of people. So, if you get a bad reaction, you might switch to a lip balm which does not contain either of these ingredients.
I think moisturizing with an all natural lip balm is a good idea in general. I wish you the best of luck. :-)