The Pick Nails are a pair of small heart shaped shovel attachments that is put on the toes of Rouge's boots. Once equipped, the Pick Nails allows Rouge to perform Dig in order to find hidden objects. They are the equivalent to Knuckles the Echidna's Shovel Claws.
The Pick Nails are located in the Egg Quarters and are needed to get the final key and complete the stage. They can be found in the Egg Fish Chamber, one of the three main rooms in the stage which is noticeable with the light shade of blue the room has and the fish statue on the wall.
Inside the Egg Fish Chamber, you will see a room with bars blocking the door way on the higher platform. Use the missile found on the smaller platform in front of the doorway to destroy the bars and head inside the newly revealed room. You can then find the Pick Nails in the back of the room.