1. Combine chicken broth and 1 Tablespoon butter in a heavy medium sauce pan and bring to a boil. Stir in grits. Reduce heat; cover and simmer for 5 minutes, stirring occasionally.
2. Mix cream cheese and Half & Half into grits. Cover and simmer mixture until almost all liquid has evaporated and grits are tender, stirring frequently, about 7 minutes.
3. Stir in green onions. Remove mixture from heat.
1. Melt 3 Tablespoons butter in a heavy large skillet over medium-high heat. Add garlic, green onions, white onions, and celery. Cook for 3 minutes.
2. Add cooked sausage and tomatoes, cook for 1 minute more, then add shrimp and sauté just until shrimp are cooked through, about 3 minutes.
3. Stir in lime juice. Remove skillet from heat.
4. Spoon grits onto center of plate. Top with shrimp mixture and drizzle with lime butter from skillet.