If you have not applied for passport, you may now apply for it on the basis of birth certificate because you have to enclose a copy of the birth certificate long with the application.
If the passport authorities dispute about the discrepancy in the birth certificate to that of the educational certificates, and issues you a show cause notice that why it should not be rejected, then you may in your reply state the facts and request their permission to withdraw the application with permission to apply afresh with authenticated documents to prove your correct date of birth.
After that you can file a declaratory suit before a civil court to declare your correct date of birth based on the birth certificate and direct the educational authorities to amend the educational certificates accordingly.
With the court order in your favor, you may apply afresh with the amended details, this will solve your issue.