Just to add some points regarding long term prevention, rather than an immediate solution.
You mention skin oils (sebum) as "gross". I would therefore guess that you are carefully washing your hair and face with shampoo, soap or other cleansers to keep them "oil-free and fresh". If you are female, you probably use make-up and other cosmetics on your face and also cleansers to take them off again (but at the minimum you seem to use lip balm).
All of these things may alter the sebum production in your skin. I want you to realize that sebum in itself is your body's own totally natural way to keep your skin and hair healthy and clean and shiny. It is no more gross than the tears that keep your eyes moisturized and dust-free or the saliva that keeps your mucous membranes in your mouth moisturized and healthy and initiates your food digestion process :-) I don't think outside substances can effectively replace your body's own function (provided your body is in good health, of course).
So I suggest to consider if any of your routines may be detrimental to your skin, and perhaps try to adjust them.
- Many people wash their hair (and face) with a weak bicarbonate of soda (a.k.a. baking soda, bicarb) solution followed by a rinse of diluted apple cider vinegar (ACV) or lemon juice, which strips away less sebum than soap does, and so normalizes sebum production after a while. You can google the exact procedure, but be aware that bicarb solution is still harsh, so dilute as much as possible and rinse out as quickly as possible. Others go even further and wash with only water. Keep in mind that your skin will need time to adjust and may overproduce for the first while (oily skin and hair with unpleasant body odor). There are ways to alleviate it (in the same articles). It does improve. Be warned however that you should not jump back and forth between methods, if you decide to do this, go all the way.
- Taking long baths or showers in hot/steamy water may also dry out your skin.
- Cosmetics may also dry out your skin especially moisturising products. Consider phasing them out. This may include some lib balm sticks, which may also actually dry out lips.
- As mentioned by others, stay hydrated. Drink water, but small quantities at regular intervals (e.g. half a glass every 15 mins) rather than big quantities at once.
- Be aware of what you eat. Some foods (e.g. sugars, refined (white) starches, processed foods, and heated or chemically-treated oils (like in fast food or cheap cooking oils) may cause your tissues (including skin) to become less than optimally healthy (unfortunately often typical student foods). Your diet should include lots of fresh (preferably raw) vegetables and fruits (mostly veggies, though). It should also include enough healthy fats (extra virgin olive oil, butter, avocados, etc.) with every meal. A moderate amount of red meat is probably good. Most modern diets or "eating lifestyles" like clean eating, paleo, banting, modernized Atkins, etc. are not too far off regarding general guidelines. (Eating healthy will also help in the body odor department, if you are worried about that).
- Iron deficiency may also cause dry skin. So again you should include at least small amounts of red meat, eggs etc. in your diet. And don't worry about the cholesterol in the foods, that recommendation is now deprecated.
- Regular vigorous exercise (working up a sweat) is also helpful in a number of ways. It improves blood circulation, gets the lymph system going which helps to detox, flushes out pores, and distributes sebum.
Sorry for the long post, seems to have lost track into to a general health sermon, and you are worried about your lips only :-)