COOK pasta as directed on package, omitting salt.
MEANWHILE, heat oil in large skillet on medium heat. Add garlic; cook and stir 1 min. or just until fragrant and tender. Stir in tomatoes; simmer 4 min., stirring occasionally. Add spinach; cook and stir 1 min. or just until wilted. Add shrimp and cream; cook 4 min. or until heated through, stirring occasionally.
DRAIN pasta. Add to skillet; toss to coat. Top with cheeses; cover. Remove from heat; let stand 5 min. or until shredded cheese is melted.