I love google...Ever heard of gout?
Long night drinking, waking up with a big sore toe... suspicious for gout to me. How old are you? Not that it matters all that much, some people have a natural enzyme deficiency that predisposes them to gout.
If that's what it is, ice prolly won't help... you'll need some medication. only one of your local scary doctors can prescribe.
Good luck.
You seem to know a bit about it...Nope. You can minimize it the natural way by drinking lots of water..