K.W.
I think there was good advice in all the replies.
I am also afraid of/hategerms(funny my house is a mess lol) and talked to someone about it, and they said I have a mild case of OCD. It doesn't help me that I also have the same dry skin you mentioned your dtep-daughter has, and I constantly have to use lotion(I have used EVERYTHING there is). I am so thankful I found this stuff at Walmart called Body Essence antibacterial hand lotion. It's alcohol free(all hand sanitizers have alcohol which dries the skin--as do most lotions...makes dry skin and rashes worse!) yet still antibacterial, so it kills the germs. I replaced the Germ-X I carry in my purse with this. Bad thing is at Walmart, I can only find it in travel size on some of the registers. Worth a try for her, though, or look at a health supplements store. Here in WA we have Super Supplements. I'm sure they have something alcohol-free that's antibacterial.
Aside from all that, my first thought when I read your request was like Angela thought that maybe she just learned about germs in school? If so, I'd wait a bit, get her off the alcohol sanitizer and away from the antibacterial soaps, and into something without it(regular soaps are actually recommended instead of the a/b ones), and if she doesn't stop soon, get her some help for OCD.
Good luck to her and you!
K. W