Peel and de-vein the shrimp. Set them aside in a refrigerator
Using medium dutch oven, heat the oil over medium-high heat. Add the flour and whisk constantly (but don't let the hot oil hit you) until the mixture is brown.
Add the celery, onion and green pepper. Saute about 5 minutes
Add the ham and continue to saute until the vegetables are tender.
Add the chicken broth, spices and herbs, and tomatoes. Stir and bring to a boil.
Add the rice and stir the mix well. Then cover, reduce heat to low, and simmer 20 minutes. If the rice is not tender simmer a bit longer.
Add the shrimp. Stir, cover and let cook for 5 minutes.