The problem with humidifiers is they cause mold and fungus to overgrow in the room, and fungus gives off a poison known as a mycotoxin. Molds are naturally occuring spores in the air, they are everywhere , and they are waiting to grow and find food (look how soon they find a peice of food on a counter for a few days.)The moisture can settle on window sills and mold can grow and eat the moist wallboard and wood.
You didn't say if yuo were breastfeeding or not.It is possible she has vitamin b deficiency. You can get liquid B drops at walmart. give twice a day.Keep in mind many kinds of medications, including antibiotics and antacids, can mess with vit b absorption. Sugar kills vit b. Fevers, traumatic injury, alcohol, IBS, internal parasites in the gut, all contribute to vit b deficiency.
You can help your vit b levels by taking probiotics like accidophilius and lactobaccilus.
It's most probable she has a bacterial/fungal infection on the skin. Deeper cracks,especailly in the center of the lower lip, are idicative of a fungal/bacterial infection. My son had these.
I would sneak into his room at night after he fell asleep and dab metronidazole on his cracks.Or, I found that mixing boric acid(found in the pharmacy by the eye solutions) with a little coconut oil and putting in the sides of mouth and on the lips can clear up cracks even better, within one day usually. Boric acid has a wonderful, natural antiseptic property against yeast and bacteria. I use the same mixture above to make vaginal night suppositories for vaginitis (either the one caused by yeasts or the one caused by bacteria/protozoa.)(I store the blueberry sized suppositories in the fridge when not in use.)
Sometimes chapping is occuring when the body is going into survival mode when it knows it's getting too low on water. it will pull the water from the skin, bowels, digestion,etc. and send the water to the organs that must keep a steady water supply to survive: brain, heart,and CNS.I doubt this is the case with your baby though, because the dehydration would be to the extreme to get to the 'cracked' stage.
Iron deficiency or allergy to the foods mommy eats can also cause it. You can try changing the laundry detg. of her sheets but I doubt that is the problem.