Spread jicama and carrot on a clean, dry dish towel with strands going in the same direction. Roll up and press towel (to squeeze out as much liquid as possible without breaking strands). Transfer vegetables to a bowl and fluff with your fingers. Add celery, mint, cilantro, chiles, and shrimp and toss to combine.
In a small bowl, combine lime juice, sugar, and fish sauce and stir until sugar dissolves. Pour dressing over salad and toss to coat, then sprinkle with chopped peanuts.
Note: Nutritional analysis is per serving.