Burned my finger while cooking. Advise to ease pain?

I thoughtlessly grabbed the lid of a thing I was cooking in the oven (400F) and burned the index finger of my left hand and a little bit of my thumb too. Having my finger in ice cold water eases the pain completely, but almost as soon as I take my finger off the ice cold water the burning pain gets back. That was about 2 hours ago. The finger itself doens't look too bad, other than the fact that I have a band of fingerprints missing, but the pain is bad enough I won't be able to get any sleep unless I ease the pain, and of course I can't sleep with my hand immersed in ice cold water... I do have an ice pack that's probably my only hope, but I wonder if there are other burn pain relievers or suggestions to ease the burning pain...? I've heard of applying butter or toothpaste to the burned area. I tried butter but it doesn't seem to be doing anything (although it may help it to get/feel worse). Any suggestions...? (I don't have any drugs or painkillers at home either...)