I have used ice and ice water for burns for years, but there are a few tricks. First, you have to leave the burn in contact with ice until it stops hurting, but you want to put it in a tea towel (thin dish towel or rag - not terry cloth). The trick is to leave it in contact with the burned area until it stops burning, about 20 minutes or so. This is for a minor burn. Once it becomes numb, take off the ice. If it starts to burn again, you need more time.
This said, you must know the risks of shock. Dumping a cup of hot tea in your lap and burning your genitals can easily put you into shock. This happened to a friend of mine and they put ice water packs on her (rags soaked in ice water) for quite a long time. I was there to see it. They sent her home with ointment of some kind. Cold stops the tissue from cooking, but you can also freeze the tissue and damage it. So, you have to use common sense. If you leave ice directly on skin for too long, it will freeze it like anything else. Check it often. If you can't take the ice, use ice water or rags soaked in ice water.
Know the symptoms and risks of shock. If you are alone and you are at risk of going into shock, call 911. Do not try to treat yourself. Do your homework, and use common sense.
Ice really helps, i burned my thumb on a tray and put it in a small bowl of ice, if you have nothing else to put on, ice is your best option.