I kind of have the same problem, and carry several little things of lip balm with me. I want to say chapstick is one of the cheapest, and that other one called Nivea. The thing is, if you want to get something fixed you probably have to spend a few dollars. I wouldn't recommend burt's bees because it doesn't work very well and is SUPER EXPENSIVE! I bought a chapstick thing from them and it was ten dollars- plus totally not worth the money. So here are my recommendations (from a person who loves lip balm):
OMG THIS WORKED SO WELL! Not only did it taste and smell good, but it really worked on my lips. If you put it on before you go to sleep your lips will be super soft and stuff in the morning.
2. Baby lips
A little expensive (Hey, it's Maybeline) but it works pretty well. This is the one I'm currently using, and I love the smell plus all the lip balms come in sheer colors.
3. Nivea Honeysuckle (yellow tube)
This smelled soooo good and it worked pretty good. This is the one you want to get if you can't spend much.
4. Exfoliating your lips! Since yours are sensitive, you need to make sure you don't scrub hard or anything, but there are two ways I do it.
a. Dampen your toothbrush and lightly scrub your lips for about 20-30 seconds. Pat dry your lips with a paper towel, then apply lip balm
b. Using extra virgin olive oil (like 1/4 a teaspoon) and mix it with about 3/4 a teaspoon of sugar. Using your finger, rub it over your lips (like massaging) for about 20 seconds. Then wash off your lips and pat dry them with towel. Apply lip balm.
Other than that, usually every store has someone who works specifically in the beauty department. (Especially little stores like CVS) Ask them and they will tell you exactly what can work with your lips.