Pinkie Pie is a little sick. That's a lie. She's sick, and more than a little. It's going to change her life forever, and it will take the power of friendship to get her through this.
Applejack is wearing a disguise. She doesn't want anypony to see her entering Manehattan's Eraser Club. She certainly doesn't want anypony to know she's having a little procedure done to remove some appendages.