You are not obliged to show your cards, since she has already shown hers. By not obliged I mean you do not need to turn your cards up in the normal course of things. She showed first, so you can muck your hand if it looses.
However, she can also ask to see your hand, as can any player at the table when a hand goes to showdown. The custom used to be the dealer would turn your hand up when any player at the table asked. This custom is changing and at almost all poker rooms the dealer now needs to call for a floor person to turn your hand up*. In this type of situation there is a good chance your hand will not be turned up by the floor person. Turning the hand up of the looser on request of the winner, is considered an unnecessary needle, and one of the prime reasons that dealers now need to call a floor person rather then turning the hand up.
*the exception is when a player exposes his cards to other players in the hand, then the dealer just shows the cards.