The skin conditions you're describing are often indicative of systemic immune issues -- and thyroid imbalanaces are often associated with skin problems. I honestly don't think bathing with dish soap is going to do anything but excessively dry out her skin (and leave it susceptible to a secondary bacterial infection). If she does have a staph infection on her skin, the best thing I know to use is very diluted tea tree oil spray and spray it on 2 times a day until things start to clear up. TTO is antifungal and antibacterial, so regardless of what the issue is, it should help clear it up.
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