Am I allowed to call the arbiter on my opponent's turn? My opponent, in their turn, was distracting me making annoying sounds. However, the arbiter said that I should wait until it's my turn when I called them. Is this correct?
You are absolutely allowed to call the arbiter when it is your opponent's turn. There are any number of reasons why this would be necessary.

To start with the most prosaic, you have filled your scoresheet and
need another one.
You are feeling unwell and need medical assistance
Your opponent has picked up a piece but isn't sure where to move it to. They are holding the piece above the board, obscuring your view of the board and distracting you.