How To Treat Chronic Diarrhea Leading To Red Rashes On Buttocks?

Hello. My one year old has a slight ear infection. She was previously on Augmentin and her diarrhea was so severe that she developed a huge red rash on her bottom because she wasn t changed every 10 minutes at her daycare. We took her off the medication. Her doctor then put her on Cefdinir. She again has has diarrhea every 10-15 minutes. Is this normal? She is supposed to be on this medication for 10 days. Now I am worried that daycare will not be changing her every 10-15 minutes again and she will develop another rash. She is taking a probiotic but nothing is working. How do I deal with this??? Please help.