Fill a large pot with lightly salted water and bring to a rolling boil. Stir in linguine and return to a boil. Cook pasta uncovered, stirring occasionally, until tender yet firm to the bite, about 8 to 10 minutes; drain.

Heat olive oil in a large skillet over medium heat. Sauté onion until tender and translucent. Stir in garlic and butter; sauté until garlic is soft and fragrant, about 1 minute.

Dissolve flour in milk; stir into onion mixture. Season with salt and pepper; simmer for 4 minutes, stirring constantly. Add cheese and stir until melted. Stir in pesto. Add shrimp, mushrooms, and tomatoes; cook for 4 minutes, or until heated through.

Add pasta and toss until evenly coated.