2002 Honda Civic - whining sound when turning/sometimes when not turning

I have a 2002 Honda Civic EX with 146,000 miles. It started making a whining/high pitched humming type noise whenever I turned. Every now and then it makes the same noise (though not as loud) when I’m just driving straight.

When I checked my power steering fluid, it was low, so I added to it. That helped with the noise briefly, but now it’s back and the fluid level is fine.

Any thoughts you have will be most appreciated.

The low fluid level most likely burned up the pump… You can either deal with the wine, and know that one day the pump will give out all together and you will lose your power steering, or get a new power steering pump now… MAKE SURE that whoever does the work flushes out as much of the old fluid as they can, so as to not damage the new pump.

Methinks that Gasrag is right.
Try putting your head under the hood and having a friend turn the steering wheel. Listen for the source of the sound. Be sure the car is in P or Neutral with the parking brake on, your friend’s foot on the brake, and stand to the side rather than in front. I would hate to have someone get run over because of a suggestion I made.

Thank you both very much, great advice all around!