Bring a large pot of lightly salted water to a boil. Cook angel hair in the boiling water, stirring occasionally until tender yet firm to the bite, 4 to 5 minutes. Drain.
Melt butter in a saucepan over medium heat. Add garlic; cook and stir until fragrant, about 1 minute. Stir in flour until a thick paste forms. Whisk in milk gradually until fully combined; bring to a simmer.
Whisk paprika, black pepper, and red pepper flakes into the sauce. Add Swiss cheese and Parmesan cheese a little at a time, whisking constantly, until melted into the sauce, 3 to 5 minutes.
Combine angel hair pasta and shrimp in a large bowl; pour cheese sauce on top.