If bled incorrectly, you can damage the new pump quite easily. Also, if the steering rack is failing, it can also damage the pump. I typically would remove both the steering rack and power steering pump together, (not difficult at all) and take them to a specialty shop in Ontario, California that actually rebuilds axles, pumps, steering racks, etc. to new.

If you are sure your steering rack is okay, then either you bought a faulty power steering pump or you didn't bleed it correctly.

I keep the cap off, turn the key to release the steering wheel, but don't start the engine and turn the wheel slowly lock to lock several times to remove all air from the system.

After that, put the cap on, start the engine and turn the wheel lock to lock listening for noise.

hope this helps.