YES! My son has the same thing since he was a toddler - he is now 5. The pediatrician had a name for it - something he has told me over and over again, but for the life of me I cannot retain that. Something about him having an allergic reaction to his sweat.
With my son his problems mainly occur in the warm weather. His feet sweat and he in turn has this reaction to the moisture & the heat resulting in painful cracks and peeling skin. The dr. said there is nothing that can be prescribed. Prevention is the best medicine.
Our nightly routine is to treat his feet with:
1. neosporin ointment (not cream) on each crack
2. Bag balm (the stuff in a square green container found in most drug stores that farmers use on cow udders) all over his feet. It mixes with the neosporin for relief and healing.
3. Cotton socks which he wears all night to keep feet moistirized, clean, and to keep the neosporin & bag balm from wiping off. Bandaids & liquid bandages DO NOT work.
Breathable shoes are imperative in the warmer months. He wears crocs most of the time. Without socks if his feet are crack-free and with socks if he has cracks.
Also keeping feet clean so cracks do not become infected with whatever funk can enter. My son frequently takes cool baths to soothe his feet before bedtime.
He has the best cared for feet in the house. It is a pain, but as long as you keep up and treat her daily - at least once a day, she should be ok.