Place noodles in a large bowl and pour over plenty of hot water to cover. Soak for 15 minutes, then quickly rinse in cold water.
While noodles are soaking, bring chicken stock to a boil in a large pot. Add tom yum paste, lemongrass, kaffir lime leaves, and galangal and boil for 1 minute. Add shrimp, mushrooms, and nam prik pao. Continue boiling until the shrimp are cooked through, 2 to 3 minutes. Stir in fish sauce and coconut milk. Turn off the heat and add noodles and lime juice. Stir to combine well. Garnish with cilantro, ladle broth over top, and enjoy.