kartik, we know exactly what you're going through. While a few people will offer things that worked for them, the only sure way to help yourself and your sister's well-being is for you to not let it ruin your lives. Exfoliative cheilitis is no reason to miss two years of college or not get a job, and it is something you can keep in check.
As others have suggested, without going crazy trying to find your own cure, you can start taking your mind off it most of the time by coming up with a moisturizing/exfoliating regimen that keeps your lips looking decent. If what you have is the same as what most of us have, your lips should look okay for at least one day after they peel. I've found that products containing petroleum jelly encourage peeling, which is good when the lips are starting to look off. Shea butter is a good and soothing post-peeling thing to put on them, for me.
For the exfoliating part, I use a toothbrush. By no means should you force any of the skin off- only get rid of the stuff that is ready to come off, and if they look fine, leave the skin alone. Your lips should not bleed when you exfoliate them, so if they do, stop. DO NOT bite or lick your lips as this will make them worse or dry them out faster. Other than that, you should be able to use your lips as you normally would without any major issues. You may notice that some foods and drinks, like breads/alcohol/tea/coffee, dry your lips out faster. You can avoid those if you wish. I usually don't worry about it, but see what works for you. Also make sure you drink a good amount of water to keep yourself hydrated in general.