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Thank you all for your responses.  I am going to try some of your suggestions
on my daughter and see which works best for her.  Following is a summary of
the e-mails I received (no particular order):

-2 said- Neutrogena Lip Moisturizer
-Neutrogena Hand cream
-3 said- Curel - the "nutrient rich, severe dry skin" lotion with a
blue-green cap.
-A homemade, fragrance free beeswax soap and lip balm along with Nivia
skin care lotion (with Q 10) with fantastic results.  The soap is so
gentle and seems to heal my skin.  I get the soap and lip balm from The
Honey Shoppe, in Tomah, Wisconsin.  The number is (608) 372-0520.  Both
the lip balm and soap are gluten free, casein free.
-MD said take cod liver oil...she took in it capsule form and within two days
there was a noticeable difference in her lips and skin.
-HYLAND CALENDULA OINTMENT
-Pond's Dry Skin.
-6 said- Blistex Herbal Answer lip balm is gf; or berry flavor
-2 said- Nivea cream
-2 said- Lubriderm- Seriously Sensitive Lotion for Extra Sensitive Dry Skin
-related to an allergy to some ingredient in some lipsticks. (My daughter's
too young for lipsticks, but thanks for the advice for those who do use
lipsticks).
-4 said- Burt's Bees lip balm  Most of their products are gluten free.
Burtsbees.com
-KARITE-LIPS    their web address is www.modeviebodycare.com.
Ingredients: isopropyl mynistate,shea butter, candilla wax, beewax,
cetyl lactate, myristyl myristate, vitamin e, aloe vera, propylparaben,
tahitian organic vanilla.
-SunDog - Citrus Flavor. Avocado Oil, Hempseed Oil, Beeswax, Citrus Oil Blend
and Rosemary Extract. Manufactured by Sue's Amazing Lip Stuff Box 64 Westby,
WI 54667.
-2 said- Keri Lotions(all varieties)
-Oil of Olay moisturizers-all EXCEPT Total Effects
-7 said- Chapstick products:Regular,Cherry,Strawberry,Mint,Ultra SPF
30,Flavor-Craze(all)    (NOTE: Also received 5 that said chapstick is not
gluten-free.  Need to research)  But One said she called Whitehall-Robins
(800-322-3129) in October and they sent her their GF list (the list is dated
Aug 2001) which includes a long list of GF chapstick products.
-4 said- Vaseline Intensive Care lotions. A Chesebrough-Ponds
product.  The phone is 1-800-743-8640.
-4 said-Vaseline lip therapy
-3 said-Eucerin
-2 said-Vanicream
-3 said-Cetaphil
-Castor oil for very dry skin
-"Aura Glow" on face found in health food store
-2 said- drink lots of water
-Walmart carries a cream that is called Udderly Smooth
-One wrote the best for dry skin is Crisco.   It is simply amazing.   I use
it all the time.  Put on a very light coat in after a shower.  Once you try
it nothing else is as good period.  However, you must rub on a very light
coat.

Thanks again to everyone for all your suggestions! Also thanks for your kind
advices!