How do I troubleshoot or fix my power steering and brake problem

The problem is more than klikely with the power steering pump. Check all fluid levels and hoses.
The first item to check within service manual diagnostics is the power steering hose.
I have attached all instructions and referenced FIGs and Notes form the instructions.
If the hoses appear to be in good shape, not kinked and not leaking, you should still replace this hose. This is with the most probable cause which is the power steering pump failure and has low pressure. You should have the codes pulled first before moving on to this step of starting to change parts. Any Auto Zone or Advance Auto will do this for free. This will help to diagnose the issue as it will bring up any electrical faults in the system. This would lead to mechanical diagnosis if there are no trouble codes. So, you would then start with the aforementioned parts replacements.
If you decide to you can go to a local Chevrolet dealer and see if service can offer any mechanical diagnostics first. They may be able to check the power steering system pressure.
If there is a difference in the brakes when turning the steering wheel at all, even with a different noise, it is highly likely that the hose or pump has failed to make or carry the proper pressure to the power steering assist.