A birthmark that hurts when shower water hits it? Dermatologist looked and was not worried. Should I get it removed or could a birthmark be sensitive

Depends. Many dermatologists would suggest removal only if the lesion might turn dangerous. If you didn't discuss the sensitivity issue, do so and see what removal would require. Removal may be technically difficult or produce a skin defect that has it's own set of problems.
Have it removed. Birthmarks may become sensitive and if it bothers u enough u shd have it removed. .