I think I just blew 450 on a power steering pump

I've been trying to fix up the third gen 4Runner I just bought, and one of the main issues was the power steering pump was the loudest of any vehicle I've ever heard, and the steering was a bit hard.

I ended up buying a pump online and having my mechanic install it, to the tune of around $450.

As soon as I picked it up from the mechanic camera it was making the exact same noise and steering feels the exact same.

I had previously seen the YouTube video about cleaning the screen, but my mechanic said the pump was definitely bad. I'm 99% sure that pump was fine, and that screen just needs to be cleaned which I will attempt to do this week.

I guess this is more of a rant post, but I have two questions for you guys:

Could the new pump be making all of this noise only because there is still air in the system?

Could a clogged screen make the pump sound like it's completely dying?

Oh, and as a bonus question, is there any way I can check the old pump now that it's out of the vehicle to see if it indeed was bad?

 

Sounds like a R&P issue, not the pump.

 

The mechanic actually told me he thinks the rack and pinion made the pump go bad, but I'm not too far of this mechanic and I'm in the process of switching.