Hey 2B,
Since I can never weigh in based on my musical ability, I might as well jump in since I'm a Dermatologist. The fissures that occur on fingertips do basically boil down to dry skin (assuming no other rash is present). As some of the posters have said, there are different ways to get dry skin. Cold is one (and heating cold air in your house even more so), dry climate..., but especially any wet to dry cycle (like washing hands). It's like leather- enough wet to dry and it cracks. The fix is "wet to greasy". Soak hands for a few minutes so they hydrate, towel off and immediately grease them up. You need to use vaseline or equivalent. The bad thing is it takes time and diligence. You'll need to do it throughout the day (remember every time you wash your hands is a wet to dry). At night, soak, grease, and put on cotton gloves (they can be found at most pharmacies). I wouldn't use neosporin only because developing contact allergies to it are very common. You can pinch the split closed and super glue over the top, but in my experience it doesn't really last long and will usually fail the first thing you grab. Avoid anything occlusive (like band aids, tape, rubber gloves) for anything but a short time, as you quickly sweat under them, and as that evaporates it is essentially wet to dry- bad (which is why your finger turns white after you wear one for a while). Now, playing with vaseline on your hands... I've got nothing for that, but the guys in front of you should watch out.