It's a tough thing to do, especially since you are adopted. You could first see if there are any public records of your birth and then begin looking for another birth on the same day around the same time. Do you know what hospital you were born at or in what city/state, most likely there are public records of your birth and a possible twin. If that fails the adoption agency records are normally sealed, however you could hire a Private Investigator to see what he/she could dig up.
This will be fairly easy to achieve if you know precisely where you were born and the exact date. You can contact the hospital where you were born and have them research their records for your birthday. If you had a twin they will know and they can let you know.