Should The Burnt Hand Be Soaked In Cold Water?

Hi, my 11 yr. old just burned her hand when trying to move a frying pan of hot oil. It spilled on her. I had her run cold water on it for about 5min. then I put on a deep cleansing skin cream on it. She said that didn't help so I have her soaking it in a bowl of ice water. This seems to be helping. Am I doing the right things or do I need to take her to the Dr.?