Cheap fix attempt- replace radiator cap. Make sure the replacement is a spring center and not a drop center type. Aha, what does that mean? Make sure the silver flat thing in the middle of the rubber face is spring loaded against the rubber and not just hanging loose. There are both types that will fit.
If the pressure relief valve stuck open, then while driving around, the air flow through radiator kept coolant from boiling, but when you stopped, the heat in the block boiled it. The steam from inside the block will push all the liquid out of the container on the fender, overflow the overflow, and make a mess. Yes, of course it happened to me, that's why you should know it could be a $7 part and not a $2000 fix.
As for the fan idea, while it may cool the radiator, it won't cool the block much, and I dare say, not the coolant in the block at all. Once the circulation stops, the fan might not help much at all.