Barnbum, I am a nurse too, and I hate gloves, so I usually don't wear them, but wash my hands even more. I swear by gold bond. And it doesn't leave my hands greasy.
Your hands will be more prone to drying out and cracking if you use those hand sanitizers, 'cause they have alcohol and are very drying. If your hands get really bad, before you go to bed, slather your hands heavily with cream and put on some cotton gloves. By morning, your hands will be much better.
Good luck!