Ever since I replaced the power steering pump it has been making a loud noise when the car starts up and when I turn the steering wheel. Also, even though I cannot see any signs of leaks, the power steering fluid seems to be leaking.
You may have a bad power steering hose. If you are losing fluid, you will see it leaking somewhere under the car or you may see a wet hose under the hood. Sometimes when the hoses get old they will collapse and not allow fluid pass through them efficiently and you will hear a squeaking noise coming from the pump when you turn the steering wheel. If your power steering pump was replaced recently it is important to get all the air out of the system by turning the steering wheel all the way to the right and back all the way to the left several times. If the noise continues after that then you may have a band pressure hose on the pump. I would have a technician inspect your power steering leak since the pump was recently replaced.