Heat oil over medium heat in a large Dutch oven. Add the cut sausage and chicken to the Dutch oven and sear until lightly golden, about 5 minutes.
Add the onion, peppers, and celery and cook until the onion is translucent and soft, stirring frequently.
Add the garlic and cook for 1 minute, stirring frequently to make sure it doesn't burn.
Stir in the crushed tomatoes, paprika, salt, cumin, oregano, basil, thyme, pepper, and cayenne pepper until incorporated.
Add the white rice and chicken broth and bring the mixture to a boil. Then reduce the heat to medium low and cover. Allow to simmer until the rice is just cooked (about 20 minutes), stirring every few minutes.
Stir in the shrimp, cover again, and let simmer for another 5 minutes, or until the shrimp are cooked (about 4 to 7 minutes depending on the size of your shrimp).