Are these: http://www.foxglovesinc.com/products/gloves/
Washable, in socially acceptable colors and grip like the dickens!
I'm betting that it feels as if someone sanded your fingerprints off of you. And, that they are always dry. Do persue with a neurologist that you mite have an autoimmune neuropathy... That's not to panic or anything, just a symptom that affects either AIPN's or diabetics to some degrees.
Get a heap of good lotion that you like [that doesn't feel greasy or sticky] and slather away! If they seem 'pruny' as well? Time to double check w/your doc or neuro about this issue. It's a AI aspect of some neuropathies.
And, yes! I'm always using 'grippy things' to help hold on to anything! About 80% of the time! It's not that I've no strength? I DO. It's just that my normal sweats and oils aren't there so there's nothing to hold onto? Especially plastics!
As for the docs? Doesn't hurt to ASK? Kindly and matter of factly. That's the best way to raise your concerns. w/o panic or stressing [even tho you are?] is the best way to get any help you mite need. Good LUCK! And, 's!!!!!!!! - j