It sure looks like a standard shimano bottom bracket tool for square taper. I bought mine from Nashbar, I think mine is half inch drive.
The 1.37 68 means it is a standard british thread, most british bottom bracket shells are 68mm and this would be one of those. (One of my bikes uses a 73mm bottom bracket.)
At 54 seconds into this video, he is holding a cartridge square taper bottom bracket like you have. And at 6:20 he is installing one.
The cartridge bottom bracket is non-serviceable, if the bearings are bad you replace it. Otherwise, re-install. Or, if you are nervous because it is 20 years old, a new UN55 bottom bracket is cheap. Match the spindle length if you order a new one.
There are some cartridge bottom brackets that are serviceable, but those are rare and cost more.