You have a long battle ahead to get your correct date of birth incorporated in your passport, more so in view of the fact that now even your birth certificate, which is the best document to vouch for a person's accurate date of birth, has an incorrect date of birth mentioned therein. Firstly, get your date of birth rectified in your birth certificate. Thereafter, on the basis of correct entry of date of birth in birth certificate, apply for rectification in your passport. This might require you to move the civil court for necessary reliefs if the authorities do not do the needful. There is no nexus between inaccurate mention of your date of birth in your passport and the fact that the age difference between you and your sister, on the basis of the date mentioned in your passport, is barely a month. The Passport Officer could not have rejected her application on this ground. Your sister may move court against him.