How can I prove that I’m really in danger in my home country?

I would suggest that you have some documents such as Police reports, court papers, medical records, or official complaints help prove your case

 In this I will say you can provide some official documents from groups like the U.S. government or human rights organizations that explain why your country is unsafe.

In this situation, if someone sent you threatening messages, emails, or left notes, bring those as evidence.