In a large saucepan, bring 4 quarts of water to a boil. Stir in the shrimp, turn off the heat and let stand until the shrimp are just firm, about 2 minutes. Drain the shrimp in a colander, and then cover with 2 cups of ice cubes to cool.
Preheat the oven to 450 degrees . Place 6 tortillas on each of 2 baking sheets (line with foil for easy cleanup). Brush both sides of the tortillas lightly with oil. Bake 6 to 9 minutes, until crisp and a shade darker. Transfer the tortillas to a rack to cool; repeat with the remaining tortillas.
Cut the avocados into 1/2-inch dice and put in a large salad bowl. Add 2 tablespoons of the lime juice and the tomatoes and toss. Add the shrimp, cheese, edamame, corn and romaine; do not toss.
Whisk the vinegar with the mint, the remaining 1 tablespoon of lime juice, the sugar, salt and pepper. Gradually whisk in the olive oil. Drizzle the dressing over the shrimp mixture, toss and season to taste.
To serve, spread each tortilla with 1 tablespoon of sour cream and top with the shrimp mixture.