Combine rice with 3 cups water, cover and bring to a boil. Reduce to a low simmer and cook 40 minutes. Remove from heat and let stand 10 minutes. Fluff with a fork and transfer to a large bowl.
Meanwhile, heat grill or grill pan to medium-high. Toss shrimp with 1 tbsp of the oil, 1/4 tsp of the salt and 1/8 tsp of the cayenne.
Thread shrimp onto skewers. Grill corn 3 to 5 minutes per side, turning 3 times (12 to 20 minutes total). Grill red onion 3 minutes per side, and avocado and shrimp 2 minutes per side.
Cut kernels from corn cobs, dice onion and avocado, and remove shrimp from skewers. Toss in bowl with cooked rice. Gently toss with lime juice and remaining 1 tbsp oil, 3/4 tsp salt and 1/8 tsp cayenne. Garnish each serving with 1 tbsp cheese.