Background check company reports can show arrests, charges and convictions. These records and (some) court hearings are public records, accessible by anyone.
You should be able to seal or expunge any arrest that does not result in a charge, any charge that does not result in a conviction, and some convictions (after a period of time).
False accusations can result in charges but charges without sufficient evidence should not result in a conviction.
It appears you need an attorney in your area to help you with the current charge and to put a halt to your sister's harassment. I suggest you keep a good record of all that your sister is doing and saying, this in case a police complaint or a civil action must be pursued against her in the future.
Good luck.