Fill a large pot with lightly salted water and bring to a rolling boil. Stir in fettuccine, bring back to a boil, and cook over medium heat until tender yet firm to the bite, about 8 minutes. Drain.
Heat heavy cream and 1 cup butter together in a large saucepan over medium heat until butter is melted. Add Romano cheese, Parmesan cheese, 1 clove garlic, salt, and black pepper; cook and stir until cheese is melted and sauce thickens, about 5 minutes. Remove from heat.
Heat remaining 1/4 cup butter and olive oil in another saucepan over medium heat. Add onion; cook and stir until softened and translucent, about 2 minutes. Stir in remaining 2 cloves garlic and mushrooms. Increase heat to medium-high and cook until soft, about 2 minutes. Add shrimp; cook and stir until firm and light pink in color, 1 to 2 minutes.
Fold shrimp mixture into sauce. Add drained fettuccine; toss to coat with sauce.
