Instead of being so blunt, you probably could have chosen your words more carefully and gotten the same point across in a more sensitive way. After all, no one likes to feel they are being condemned or looked down upon. How would you have felt if she had attacked you?
Few things can get us in as much trouble as our words and few things can be more helpful to others, if we learn to speak wisely and out of love. The Bible says, "A word aptly spoken is like apples of gold in settings of silver" (Proverbs 25:11). It also says that "Reckless words pierce like a sword, but the tongue of the wise brings healing" (Proverbs 12:18).
Don't let this rift between you and your cousin continue; the longer it goes on, the worse it may get. Instead, take the first step by telling her that you are sorry if you offended her and you hope she will forgive you. If there was truth in your words, trust God to show your cousin where she is wrong.
In addition, ask God to teach you through this experience. Perhaps He wants to show you your need to discipline your tongue or to be more loving toward others. He may even be showing you that you need to commit your life to Christ and if so, open your heart to Him without delay.