Add butter to a large skillet, set over medium heat.
Once melted, add the onion/pepper mixture & celery to the skillet tossing gently to coat. Sautee the veggies, stirring occasionally, for 5 minutes.
Add the shrimp to the skillet, and stir to evenly incorporate. Sprinkle the seasonings evenly out over top, and stir until everything's evenly mixed. Let the shrimp & veggie mixture simmer for another 5 minutes.
Stir both cans of soup and the cooked rice into the shrimp mixture until smooth and well mixed.
Taste the mixture & add any extra seasonings you may require. No extra's necessary though if you're happy with the taste.
Transfer the mixture to a casserole dish, scraping the skillet as necessary. Bake the shrimp & rice casserole uncovered for 20-25 minutes at 350°.
Remove the baked casserole from the oven, and let it rest for 2 minutes, to set up and thicken slightly.
Ladle it into bowls or onto plates, and serve immediately.