This sound a whole lot like eczema
. Eczema is an inflammatory condition of the skin that occurs because the skin is lacking the ability to retain its natural levels of moisture. This leads to redness, cracking, and itching that tends to come and go in waves, worse in cold dry weather or with exposures to irritating substances. Eczema can just occur on the hands like your daughter is experiencing.
The mainstay of treatment of eczema includes frequent moisturizing. It is essential to use a thick, greasy moisturizer like hydrolated petrolatum. Standard lotions and creams are not thick enough to properly trap in the skin's moisture and provide protection. Avoiding overwashing the hands is also important, and making sure to apply moisturizer after washing is critical.
Steroid creams are usually needed to get things under control. Although 1% hydrocortisone cream is a steroid, it is the weakest steroid on the market. Once eczema gets very inflamed, stronger creams are needed, and these are available by prescription only.
I would suggest talking to your daughter's pediatrician
. They will be able to confirm the diagnosis and they will prescribe the right medications and give you instructions on how to use them properly.