Here's a quick check, and it might solve your problem. Pull the lower radiator hose at the water pump, and find a pipe coupling about the right size to slip into the hose and clamp into place, probably one for 1 1/4" pipe or so. Adapt it down with a series of reducers until the nozzle of an air blow gun can be threaded on, usually 1/8" or 1/4" pipe.
Now, pull the upper hose off at the thermostat housing off, and aim it in a direction that won't spray rusty crud all over the engine compartment- - -maybe out over the fender or somewhere. Fill the radiator with water, then goose air into the bottom tank with the blow gun, just a quick 1-second blast or so. The shock of the air meeting the radiator full of water will blow any crud out of the radiator core and send it flying, usually without springing any leaks in the core. That's what a radiator shop calls a "reverse flush" and it's exactly how they do it. All it takes is a little time and pocket change scavenging up and assembling fittings. You'll be amazed at the crud that blasts out of the radiator!
Jerry
