For the pico de gallo: Combine the tomatoes, jalapeno, onions, cilantro and lime juice in a small bowl. Season with salt and pepper. Set aside.
For the burritos: Heat the oil in a large nonstick skillet over medium-high heat. Add the chorizo and cook, breaking it up, until it is slightly crisp, about 5 minutes. Remove to a paper-towel-lined plate using a slotted spoon. Add the hash browns to the skillet and cook, stirring occasionally, until the potatoes are golden brown and crisp, 8 to 10 minutes. Beat the eggs in a medium bowl until frothy. Sprinkle with salt and pepper and a couple dashes of hot sauce. Pour the eggs over the hash and cook, stirring, until the eggs are fluffy and just set, about 3 minutes. Remove from the skillet and keep warm. Wipe out the skillet and return it to the heat.
Warm the tortillas one at a time in the skillet.
Build the burrito by layering the avocado, egg mixture, about a tablespoon of pico de gallo and a sprinkle of cheese. Fold in the two sides and roll up tightly. Garnish with the reserved cilantro leaves and serve with additional pico de gallo and hot sauce on the side.