Heat 1 tablespoon of the oil in a large nonstick frying pan or wok over medium-high heat until shimmering. Meanwhile, pat the shrimp dry with paper towels. Add the shrimp to the pan, season with salt and pepper, and cook, stirring occasionally, until pink and just cooked through, about 2 minutes. Remove to a plate; set aside. Add the remaining tablespoon of oil to the pan and heat until shimmering. Add the kimchi and chile paste and stir-fry until fragrant and heated through, about 1 minute. Add the rice, fish sauce, and soy sauce and season with salt. Cook, stirring constantly, until the mixture is heated through, about 3 to 4 minutes. Push the rice mixture to one side of the pan, add the eggs, and cook, stirring occasionally with a rubber spatula, until almost set, about 2 minutes. Season the eggs with salt and pepper. Remove the pan from heat, fold the eggs into the rice mixture, add the reserved shrimp, measured lime juice, and sesame oil, and stir to combine. Taste and season with more salt and lime juice as needed. Sprinkle with the scallions and serve immediately with the lime wedges.