Police detained me under false information

I'm 15M from NSW and recently Someone online that I had beaten at a video game or something decided to dox me

They then call my local police station and say that I said I was going to kms they sent the police a screen shot of a letter that I had supposedly posted in a discord server with the user at the top cut out of frame

Then at 5am in the morning the police and an ambulance are at my door telling me I have to go to the hospital.

Note the only thing they have at this point is the fake letter that was so basic anyone could have made it.

Unfortunately due to the mental health act of 2009 it allows the police to brake all laws and procedures if they suspect you have a mental health problem eg. Illegal search, detaine and arrest with no reason, no probable cause or reasonable suspicion needed.

I ended up going to the hospital and getting cleared. I have the hospital discharge report that sides with me as well as othe evidence.

I want the police to add to my record that it was a fake/false report but there refusing to do so because they don't have proof that it was

What happened to innocent until proven guilty the police have done no investigation and are refusing to do anything to help What do I do?