Am I allowed to shuffle my hand when ever I want?
When you are playing a game, you can reorder your hand whenever you want. Your opponent is not supposed to know which card is which in your hand unless your hand is revealed.

If a spell allows you to make your opponent discard a card, it will either say


  [Player] discards a card at random from their hand.


In which case, you should shuffle the hand before allowing them to chose a card from it.

Or, it will say


  Look at [player]'s hand (or "[Player] reveals their hand"). You choose a [quality] card from it. That player discards that card.


In that case, they are looking at your hand, so they will definitely be able to know what card they are choosing.