I agree with dabnis. Sounds like a head gasket. Hopefully the head isn't warped.
A compression test would probably show which cylinder(s) are low, indicating a leak into the water jacket. I can't think of anything else that would pressurize the coolant system that fast. Head gasket isn't too severe to change as long as the head is sound and not warped. A machine shop can check the head for being warped and if not too severe it may be trued up.
If so, valve clearances should be re-set, even if you just replace the gasket with no head work being done. Not likely the block deck is warped but it can be checked with a good sharp straight edge, at least for starters. A dial indicator, if there is a solid surface to mount it on? might show any variences?
Not sure exactely how to mount it, maybe someone with machine shop experience could advise?