Noah,
More than likely the water pump is ok if its not leaking. There is a oraface on the bottom side of the pump that will leak when the pump no longer will hold water. Just look for a drip or wet spot under the engine.
Take the radiator out and reverse flush it. Use high pressure (120 lb or so) air hose and chuck. Wrap a rag around the chuck at the lower outlet. Have a steady water flow to keep the radiator refilled. This will not clear all the flues but maybe a sufficient number of them.
Open the block's drain plug and flush the block with water entering the outlet to radiator (remove the thermostat). Use high pressure air hose and chuck at the block's drain.
Get a new thermostat 170 or 180 degrees. Either one will not make any difference in the overheating problem.
Do check the fan belt for slippage.
Be careful when grabbing the fan blades. Never try to turn the engine by grabbing them. A thing of beauty is a fan turing in a true plane. Not so when a blade is out of whack. It doesn't take much to do this.
While the radiator is out clear the bugs and whatever from the fins. Blow back through it with the air gun and water hose. Straighten any bent fins.
After doing all this you find that it still overheats, have the radiator boiled and rodded, re-cored or get a new one. Flushing the block is sort of mandatory but can only be properly cleaned by a machine shop that will drop it in a solution for that purpose. You'll be surprised at the amount of crud that will come out using the simple method described above. Do it until the water clears up. Thats all you can do without taking the engine out.
Check the bottom radiator hoses to make sure that one or both are not obstructed and/or collapsing. Especially if it's a one piece replacement hose.
Good luck,
Charlie
BTW: I don't encourage you to use any "flush" chemicals in the radiator. Generally, it only makes the problem worse.