In a large bowl, toss the shrimp with Old Bay seasoning and olive oil until well coated.
Heat a large skillet over medium-high heat. Add the seasoned shrimp and cook for 2-3 minutes on each side, or until they turn pink and opaque. Remove from heat.
Warm the flour tortillas in a dry skillet or microwave for a few seconds until pliable.
To assemble each burrito, place a portion of rice, black beans, corn, diced tomatoes, avocado, lettuce, and shrimp in the center of a tortilla.
Sprinkle with shredded cheddar cheese.
Fold in the sides of the tortilla and roll it up tightly from the bottom to the top.
Repeat with the remaining tortillas and ingredients.
Serve the burritos with lime wedges on the side for squeezing over the top.