I am playing on an elemental shaman.

I looked up shields on the auction house, but autogear said in the tooltip that elemental shaman's should not use shield!

Then I tried to look up staves and autogear said it was not valid weapon for a shaman.

Then what am I supposed to use?

You must be using a spec override. Elemental does not have weapons defined, which makes it use weapons type "any" with this line:

weapons = AutoGearCurrentWeighting and (AutoGearCurrentWeighting.weapons or "any") or "any"

Please enter chat command /ag spec and show the output.