Allergies to latex are so common that most of the health care professionals in my area (major glove users) have switched to non-latex kinds. They seem not to be much different in price, from what I've seen in retail outlets, so perhaps you could get a different kind at least for a temporary trial.

If you are stuck with using latex, be aware that many common hand lotion ingredients will cause very rapid degeneration of latex. In fact - if you've been using lotion recently you could be destroying the gloves (with your lotion) rapidly enough to expose yourself to whatever the gloves are meant to exclude. (The latex may not break, but still could become permeable.)

Any persistent crud around the nails, hands or feet, should trigger the suspicion of fungal infection. Even if it's not the "original" cause, fungi grow so persistently in callous that it may jump in as a secondary problem. Any good anti-fungal (athlete's foot or "jock itch") spray or power can be used to at least verify that there isn't such infection.

A little supplemental vitamin E sometimes improves general skin health, and won't hurt if used in moderation.

Since the tissue around the nails is mostly callous - i.e. dead meat - there's not much you can do to bring it "back to life" with any kind of lotion. HEALING the area, by avoiding exposure to what causes it, and knocking out any infectious invasions of the tissue, are about all that usually helps. Lanolin, aloe, and shark oil are the commonly recommended "emolients" in such cases, but I'm not sure any of them work much better than bacon fat.

(Note: above is strictly a non-professional opinion. If you really are concerned, professional assistance is often something to consider.)

John