Difficulty sleeping
It is difficult to say exactly why your daughter is having issues with excess heat, without knowing a full case history. This is almost certainly linked with her sleep problems, so once you have dealt with the heat the insomnia will likely be resolved as well. I know that in Traditional Chinese Medicine (TCM) excess heat is treated as a separate and underlying issue that may trigger other symptoms, such as the eczema that your daughter is dealing with.
A TCM practitioner typically utilises a combination of herbs and acupuncture or acupressure to rebalance the body. Ayurveda, the traditional Indian medicine system, has a fantastic cooling herb which is also very nutritious. Shatavari (asparagus racemosus) has a specific affinity with female health and helps with hormone regulation, so this nourishing and cooling herb would be a great choice to support and prepare your daughter in the years leading up to the changes she will experience with the onset of puberty. I like to take this herb as a tea, using 1 teaspoon and steeping it in boiling water for three to five minutes. It is quite mild and pleasant tasting.