So bummed, maybe need some help...my sim is constantly being falsely accused.

Take a look at your sim's friend list. Anyone whom you don't want to bother having to interact with on a regular basis to maintain a very high relationship - cheat the friendship bars down.

Stick to a select few friends, don't make many. I've found that whenever a relationship deteriorates to 'lost a friend' status, I get a lot of those false accusations. It's too easy to make friends in this game, and too easy to lose them.

I also remove celebrity status now whenever it's earned.