94 Chrysler Concorde overheating

I just bought a 94 chrysler concorde 3.5 engine, 175k miles. It ran great for almost a week but then started overheating. I hooked up my pressure tester and it holds pressure so im assuming no leaks. I put a new radiator cap on it and it still went hot. The steam and water end up comming out the overflow. I did test the thermastat and it was good. I guess the only things left are the water pump and the radiator. I did remove the upper radiator hose going into the engine and turned the car on. It was comming out both the engine and radiator hose. Led me to believe that the water pump is pushing water. Or am I wrong? Any help would be greatly appricated. Thank you