The threat may or may not be true. To check if your PC is compromised or not you have lot of things to check.
1. check for any newly installed software. Update your anti-virus and perform a scan. Uninstall every suspicious installations.
2. Check registry for malware entries.
3. Check system logs
4. Open netsh in a terminal and monitor all connection and check for any malicious connection is established to some remote IP by any unknown softwares.
5. Check for CPU, RAM, and Network usage while idle, if there is any malware installed usage will be high.
6. Check browser, Uninstall any newly installed extensions and toolbar. Its always a good idea to reinstall browser and use "logout from everywhere" option in social media accounts.
7. Do not trust public WiFi. They can be a honeypot, monitoring all your activities.
8. Reset your router, Routers and Modems can be configured to monitor you by connection to hacker's proxy or some sort of monitoring network.
These are the basic things you can do. However if the hacker is smart enough, he may have created a malware smart enough to remain undetected. Best thing you can do is report the person to authorities.