I think you need to sit down and have a good talk with your cousin and explain to her that you are in the process of trying to make some life changes, and that you want to be sure that your past is behind you. Is she Muslim too? Remind her of the following hadith:
Abu Ayoub said:
“I have come to ask you about a Hadith concerning keeping secret other people’s errors. You and I are the only survivors of those who heard it.” Uqbah said:
“Indeed, I heard the Prophet (peace and blessings of Allah be upon him) as he said, ‘Whoever keeps secret a shameful deed done by a Muslim, God will grant him His cover on the Day of Judgment.’” Abu Ayoub said,
‘This is true.’
Ask her kindly to keep your secrets, and insha'Allah not only shall she keep yours, but you will keep hers.
Here is a list of duas for forgiveness:
http://www.islamawareness.net/Dua/forgiveness.html