I usually use disposable powderless nitrile gloves, which you can find at B&H and other places. I've also taken to using them for loading sheet film--no more fingerprints.

One thing you might be noticing is that when you get chemicals on your hands, you tend to wash your hands more, or at least I do, and this can cause your skin to dry out.

Some people have an allergy to metol (which is actually an allergy to impurities common in metol, rather than to the metol itself), so this could be another possibility, if you are using a metol developer.