Shred or dice cooked chicken into small pieces. Set aside.
Heat olive oil in a large skillet over medium heat. Cook onion and celery until onion becomes translucent, about 5 minutes. Stir in garlic, salt, and black pepper, and cook another 30 seconds.
Pour in chicken broth and canned tomatoes with all their juices. Bring to a boil.
Then add pasta. Stir to fully coat the pasta in the liquid. Bring back to a boil. Reduce heat, cover, and let simmer for 10 to 13 minutes, stirring intermittently, until pasta is al dente.
Reduce heat to low and add buffalo sauce, cubed cream cheese, and shredded cheeses. Stir until cheese is fully melted and incorporated.
Stir in shredded chicken.
Serve warm topped with a drizzle of ranch or blue cheese dressing, as well as crumbled blue cheese or feta over top. The pasta sauce will thicken as it cools.