Clean the shrimp by removing heads and shells but tails intact, reserve the heads and the shells. Discard the vein. Set aside.
Smack one of lemongrass with back of your knife to release its fragrance.
Heat oil in a soup pot over medium high heat, add the reserved shrimp heads and shells, and the one smashed lemongrass. Saute together for 3 minutes. Add chicken stock and galangal, let it boil first and then simmer over low heat for 20 minutes. Strain the stock and discard the shrimp heads & shells, lemongrass, and galangal pieces.
Slice the other lemongrass thinly.
Pour the stock back to the pot over medium high heat, add the sliced lemongrass, chili, lime leaves, and shallot, and bring them to boil. Add shrimp, mushroom, and tomato, and continue to cook. Season with fish sauce. Remove the pot from heat and add the lime juice.