In a small pot, cook rice according to package instructions. Meanwhile, in a small bowl, stir together fish sauce, lime juice, and sugar until sugar dissolves. In a large skillet, heat 1 teaspoon oil over medium-high. Add shrimp and cook, stirring occasionally, until opaque throughout, 3 minutes. Transfer shrimp to a medium bowl and return pan to heat.
Add 1 teaspoon oil, scallion whites, bell pepper, and corn to pan. Cook, stirring occasionally, until pepper is crisp-tender, 3 minutes. Add fish sauce mixture and coconut milk, bring to a simmer, and cook 1 minute. Return shrimp to pan, add scallion greens, and cook until shrimp is heated through, 1 minute. Top with basil and serve with rice and lime wedges.