Heat the butter in a 3 quart saucepan over medium heat. Add the onions and cook until tender, stirring occasionally. Add the shrimp and cook until they're cooked through. Stir in the chilies, half the pimientos, soups, cream cheese, and white pepper and cook until the cream cheese is melted, stirring occasionally. Remove the saucepan from the heat.
Divide half the shrimp mixture among the tortillas. Roll up the tortillas and place, seam-side down, into a lightly greased 3 quart shallow baking dish. Spoon the remaining shrimp mixture over the filled enchiladas. Sprinkle with the remaining pimientos and the cheese.
Bake at 325*F for 30 minutes or until the enchiladas are hot and bubbling.