This might sound harsh, but it once you realize it, it really helps. Everyone in your life will eventually hurt you (even if it's just a minor thing) except God. Think about it. It's true. No one is perfect and only God can be our rock to stand firm on. No one else is sturdy enough for us. Yes, we can have beautiful relationships with family members and friends but because they are humans, they will eventually hurt us...sometimes without even knowing it.
But I don't think that your sister did the right thing in telling others your business. I think that's wrong and you cannot trust her. It takes a lot of time to rebuild trust and she just blew it to pieces by breaking it.
I think you need to keep a distance, don't avoid her, she is after all, family. But be careful and use discretion.
Also, the first paragraph is to let you know that you can trust others. You just need to realize that just because someone does something wrong, it doesn't mean that they shouldn't be trusted. It's human nature to be wrong at times.
What your sister did wasn't right, I'm not condoning it, but don't think that just because others might hurt you in the future, you cannot trust them. It's inevitable that others will do you wrong. That's just how life in a sinful world works, unfortunately.
Remember when Peter denied Jesus three times? We know that Peter loved his friend, Jesus, but he still did wrong in denying him. Why did he do it? Because humans are not perfect. He was afraid.
I remember when I realized all this, it was like a huge weight was lifted off my shoulders. I no longer longed for a perfect man but I realized that my future spouse wasn't going to be perfect. Even my relationship with friends and family changed. I don't expect so much from them now because I know they are on the same boat as I. We are all humans and in dire need of a savior. I can't depend on them for acceptance and love 100%. I can get some of it from family but not the amount that I need. I can only get that from the Lord Jesus.
I hope this made sense.
Blessings to you my dear friend! I'm sorry you had to go through all this again.