Had the same problem on my 1991 accord. Replace the thermostat, gasket, and radiator cap. Also, get a gallon of coolant if your current coolant has been in there for more than three years. The thermostat is in the engine block. Simply drain coolant, remove the radiator hose from the engine - the hose that goes from the bottom of the radiator into the engine. There may also be a small spount that bolts into the block, remove the bolts and there is the old thermostat.
There are 2 fans that would be running while you are driving and that is normal... the compressor fan if you have the air conditioner running and the radiator fan runs to help keep the radiator cool while the engine is on.
Check the rotor and cap. They may be cracked.
How's the water pump?
A hole in the radiator would do that, or a damaged radiator cap. It could be a cracked engine block that is allowing cylinder pressure into the cooling system, pressurizing the water until it breaks through a weak spot in the radiator.
Cracked head or leaking gasket. The suction is created on the downward stroke of piston during intake stroke.
Try replacing the radiator fuse relay
if you have heat and and it is working OK. and if you squeeze the lower radiator return hose and feel water flowing. most likely it is the electronic fan not coming on.
Can be leaking from a hose not secured properly or a hole in the system.
The cooling fan should run continuously when the A/C is on. See if it is running, and if not check the fuse, and thermal relay. If they are good, see if the fan motor itself it good. If all this checks out, the drain and flush the radiator with a chemical flush. Also make sure the front of the radiator is free of debris.
Thermostat needs to be replaced, it is not opening (most common). Is electric fan on radiator running normally from time to time?
It sounds like you have cracked the heads.......if you're lucky maybe all you'll need to replace is the head gaskets and even that is expensive. Look to spend at least $1500. or more if the heads are cracked.
No paticular order. Head gasket, cracked head, cooling fan not running because of bad fan or sensor, plugged radiator, bad radiator cap, system air locked, leaves or something blocking the front of the radiator,