Yes you can take jewelry on a plane in both your carry on luggage as well as checked baggage.
You can also wear Jewelry on the plan if you want too as well.
Although if you do have metal Jewelry and are wearing it when going through the metal detector it will set the metal detector off.
So you may want to remove the Jewelry before going through the metal detector.
Also if you have Jewelry when your carry on luggage goes through the metal detector and it's metal the metal detector will be set off as well.
Then your carry on luggage will likely be searched.
But if you have nothing bad in the carry on luggage then nothing will go wrong.