Overheating
 

I'm currently having some difficulties trying to get my cooling system up and running. When I had bought the car, the guy mentioned it had a radiator that needed replacing. I didn't think much of it and bought a new radiator and thermostat and threw put it all together. When I took the car for a test drive it lost heat from the fans and started overheating and when I opened the hood it was pushing out of the thermostat cap. The hose to the radiator was very firm and it was trying to pump fluid into the reservoir. I thought maybe it was the water pump but I took it off to inspect it, and the water pump is in great condition. I checked the thermostat in boiling water and it opened up fine. I even checked the heater core to see if there was a blockage but it had flow going in both directions. Can someone please help me? I'm not entirely sure where to go from here

Did you try leaving the radiator cap off.
And start up your car. If you see coolant shoot out of it or bubble.

I think you got snookered and bought a car with a bad engine.

If you test the cooling system with it full cap off and it shoots coolant out then you need a rebuild.

I'll start the car up tomorrow with the rad cap off and see what it does. That's exactly what I was hoping not to hear but someone had to tell me. Thanks, I'll keep you posted!

I think your water seal is no good. You need a rebuild.

Okay so the pressure is still building up. Looks like you were right, I'll be looking for a new engine.

You necessarily do not need a new engine,just a rebuild.
If you feel you can do that yourself you may want to research REBUILD threads and the cost of parts.

Then there is always the other avenue of getting someone to take on the task of rebuilding with a reputable shop.They can be found on here as well.

^Agreed.
OP...a failed coolant seal is (roughly) the rotary version of a failed head gasket. Unfortunately unlike a piston engine, replacing the coolant seals require complete disassembly of the engine. But it does NOT mean a new engine and the rotary is pretty simple. You buying another used engine for a blown coolant seal is one solution but probably not the smartest.

I think you better off rebuilding it. Is cheaper.
You won't know what you get when you buy another one.