Do the rules specify that you must pick an item you draw? Since the amulet is a double edged sword I would rather not have to deal with it.
Yes you do pick up every item that you draw. However as long as the item does not say it can't be dropped there is nothing preventing you from dropping it.
In the case you mention the amulet (Amulet of the Ages is the full name) gives +1 to all stats when you get it and -3 to all stats when you lose it. Which is something to remember as there are plenty of cards you can get which do more harm to you then good. Als
Drawing Omen, Item, and Event Cards
If the room has an item symbol (a bull’s head ), draw an item card. Read it out loud. Place it face up in front of you; you now have the item in your possession. (You’re carrying or wearing it.) You can use the item once immediately and once on each of your turns, unless the card says otherwise.